A Comprehensive Analysis of Flexibility Options to Integrate

A Comprehensive Analysis of Flexibility Options to

Integrate High Shares of Renewable Electricity in a

European Power Network

Dissertation

zur Erlangung des Doktorgrades

der Naturwissenschaften

vorgelegt beim Fachbereich Physik

der Johann Wolfgang Goethe - Universitat

in Frankfurt am Main

von

David Peter Schlachtberger

aus Starnberg

Frankfurt 2017D 30

vom Fachbereich Physik der

der Johann Wolfgang Goethe - Universitat als Dissertation angenommen.

Dekan: Owe Philipsen

Gutachter: Stefan Schramm, Martin Greiner, Holger Podlech

Datum der Disputation: 20.12.2017

Fur Rhea

Contents

1 Introduction 11.1 Conventional Energy Sources: Limitation of availability and climate change 2

1.1.1 Fossil Fuels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.2 Nuclear Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.3 Climate Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Renewable Energy Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2.1 Wind Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2.2 Solar Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2.3 Hydro Power Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.2.4 Biomass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.3 Energy Storage Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.3.1 Pumped Storage Hydro Power Stations . . . . . . . . . . . . . . . . 13

1.3.2 Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.3.3 Hydrogen storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.4 In this work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2 Integrating Renewables with Backup Flexibility Classes 172.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2.2 Modelling dispatchables . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.3.1 Development of dispatchable capacities . . . . . . . . . . . . . . . . 24

2.3.2 Aggregation benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.3.3 Slow capacities going out of use . . . . . . . . . . . . . . . . . . . . . 27

2.4 Model sensitivities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.4.1 Power capacities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.4.2 Missing energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.4.3 Ramp rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.6 Comparison to the current German system . . . . . . . . . . . . . . . . . . 32

2.7 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.8 Appendix: Modelling details . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.8.1 Unserved hours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.8.2 Sensitivity to capacity weights . . . . . . . . . . . . . . . . . . . . . 35

2.8.3 Sensitivity to dispatch weights . . . . . . . . . . . . . . . . . . . . . 36

3 Backup Flexibility and Storage 373.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

v

Contents

3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.3.1 Comparison with the previous model . . . . . . . . . . . . . . . . . . 40

3.3.2 Addition of storage technologies . . . . . . . . . . . . . . . . . . . . 41

4 Backup Flexibility, Storage, Hydroelectricity and International Transmission 454.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.2 Methods: Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2.1 Objective function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2.2 Power balance constraints . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2.3 Generator constraints . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2.4 Storage operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.2.5 Inter-connecting transmission . . . . . . . . . . . . . . . . . . . . . . 48

4.2.6 CO2 emission constraints . . . . . . . . . . . . . . . . . . . . . . . . 49

4.2.7 Software implementation . . . . . . . . . . . . . . . . . . . . . . . . 50

4.3 Methods: Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.3.1 Network Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.3.2 Time series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.3.3 Capacity layouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.3.4 Geographic potential . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.3.5 Hydroelectricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.3.6 Non-renewable generators . . . . . . . . . . . . . . . . . . . . . . . . 52

4.3.7 Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.3.8 Cost assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.4.1 Total costs as function of line volume constraints . . . . . . . . . . . 54

4.4.2 Energy mix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.4.3 Spatial distribution of infrastructure . . . . . . . . . . . . . . . . . . 58

4.4.4 Marginal prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.4.5 Line volume shadow price . . . . . . . . . . . . . . . . . . . . . . . . 63

4.4.6 Dispatch time series . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.5.1 Comparison to the literature . . . . . . . . . . . . . . . . . . . . . . 64

4.5.2 Limitations of the study . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5 Sensitivity Analysis 715.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.2 Sensitivity to policy constraints . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.2.1 Onshore wind potentials . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.2.2 CO2 emission constraint . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.2.3 Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.2.4 Brexit / network topology . . . . . . . . . . . . . . . . . . . . . . . . 79

5.3 Sensitivity to cost assumptions . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.3.1 Solar capital costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.3.2 Battery capital costs . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.3.3 Hydrogen storage capital costs . . . . . . . . . . . . . . . . . . . . . 86

vi

Contents

5.3.4 Onshore wind capital cost . . . . . . . . . . . . . . . . . . . . . . . . 875.3.5 Offshore wind capital cost . . . . . . . . . . . . . . . . . . . . . . . . 885.3.6 Onshore and offshore wind capital cost . . . . . . . . . . . . . . . . . 89

5.4 Sensitivity to changes of physical input parameters . . . . . . . . . . . . . . 895.4.1 Different single weather years . . . . . . . . . . . . . . . . . . . . . . 895.4.2 Multi-year optimization . . . . . . . . . . . . . . . . . . . . . . . . . 935.4.3 3h sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.5 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

6 Conclusions 976.1 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 976.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Zusammenfassung 109

Bibliography 117

Acknowledgements 119

vii

1 Introduction

Different forms of energy have been used for a long time to support manufacturing pro-cesses, e.g. via water- and wind mills or the steam engines invented during the 18thcentury. These energy sources were only usable locally, directly at the energy productionsource, and only with the invention of electricity it became possible to centralize the en-ergy production and separate it from the consumer as the electricity could be transportedthrough a network. These networks were first established at the end of the 19th century,and have been growing significantly since then.

Parallel to the growth of the electricity networks and the increasing availability of energythrough these power grids, the energy demand has been rising, from its first commercialuse for electric lighting up to full home control possibilities at current date. This rise indemand required to tap new resources for energy production. While at the end of the 19thcentury, electricity was mostly produced in coal- and oil-fired power plants, technologicaladvances let to the construction of the first nuclear power plants in the middle of the20th century, that could produce even larger amounts of power in a single plant, thereforeleading to a further centralization of power generation and thus an even larger extend ofthe power transportation grids.

This “new” technology was thought to be a clean replacement for coal as the mainsource of energy, as it had become clear already in the middle of the 20th century thatcoal emits large amounts of smog and respirable dust, clearly visible in the increasinglayer of grime that covered buildings and streets in industrialized areas. Additionally,it became apparent that fossil fuels also release significant amounts of greenhouse gasessuch as CO2. Nuclear power, in contrast, did not release any such pollutants and it wasonly realized in the following decades that the long-lived, highly toxic and radiative wastefrom spent nuclear fuel and the decommissioning of old plants is difficult and expensive tostore safely. Furthermore, it became evident that, if the full life cycle of a nuclear powerplant including everything from Uranium mining to the energy intensive decommissioningprocess is considered, nuclear power still causes significant amounts of CO2 emissions.

Only at the beginning of the 21st century, the impact of the greenhouse gas emissionon Earth’s climate became evident, albeit indications for its disastrous impact had beenobserved already previously. The increase of CO2 in the atmosphere leads to a drasticclimate change, which in its onset can already be detected at present day in the increaseof the average water temperature [1] in the oceans and a dramatic rise in extreme weathersituations as well as in the deglaciation and the melting of the polar ice shelfs [2, 3].

As an answer to this issue, several industrialized countries signed a treaty in Paris in2015 [4], announcing to reduce the global CO2 emission by humankind to 40 gigatonnes ofCO2 per year, trying to limit the global average temperature increase to 2◦C. To achievethis goal, it becomes even more urgent to extend the energy production through energyresources that are CO2 emission free and sustainable. However, at the current state theenergy mix of most countries is still dominated by fossil, conventional energy sources, ascan be seen for example for Germany in Fig. 1.1: More than 40% of the energy mix in

1

1 Introduction

Figure 1.1: Electricity mix in Germany in 2015 as an example for the diversity of energy sourcescurrently used within Europe and the world. Image credit: BMWi

Germany in the year 2015 was still provided by coal plants, and over 50% originates fromcoal and nuclear plants together. Additionally, about 17% of the remaining energy mixoriginates from other, non-renewable sources like natural gas or oil, and only about 30%of the energy mix is provided by renewable energy sources. Even though this amount isincreasing slowly, there are still several issues to be solved which will be addressed in detailin this work.

1.1 Conventional Energy Sources: Limitation of availability andclimate change

Besides the problematic issue of the CO2 production and the waste storage and decommis-sioning of old power plants, there are also economic issues with the conventional energysources, as all these sources are limited and can either not at all or only extremely energy-inefficiently be replenished. In the following the main conventional energy sources willshortly be introduced with respect to their energy production mechanisms and issues.

1.1.1 Fossil Fuels

The fossil fuels used in modern power plants are natural gas, hard coal, lignite, and oil.They are formed naturally if plants or animals are buried under anaerobic conditions andremain under high pressure for millions of years. Due to this very long formation timescalethey cannot be replenished on a timescale that is relevant for human needs and thereforeare considered to be finite resources. Oil and natural gas are both hydrocarbons, whilecoal is pure carbon (with contaminants).

Oil usually coexists with natural gas in the same deposits, as they are both made inthe same process. They are formed from dead algae and other small micro-organisms that

2

1.1 Conventional Energy Sources: Limitation of availability and climate change

were deposited at the ground of the oceans, where there is basically no oxygen, between100 and 400 million years ago. During geological processes in the crust of the Earth, thesesediments are transported to larger depth where the pressure and temperatures are highenough to transform the fossilized biological matter into oil and gas. Similarly, coal ismade from dead biological matter at similar epochs, however, these matter is not rottingat the ground of the ocean but instead in oxygen-free swamps and gets compressed slowlyif more and more material is deposited on top. Hard coal is formed earlier and thus hadmore time to be compressed and purified, while lignite is formed on shorter timescalesbut is contaminated by mostly sulphur but also other trace elements. Therefore, lignite isthe least energy efficient and the most CO2 contaminating of these fossil fuels, albeit it isusually the easiest to mine.

In electrical power plants, these fossil fuels are oxidized (i.e. burned) to generate heatthat is used to drive an electric generator via a Carnot-process. During this oxidization,carbon is transformed into mostly carbondioxid (CO2) and usually some by-products like,for example in the case of natural gas, water:

CH4 + 2O2 → CO2 + 2H20.

In the best case scenario of energy efficiency, there are no by-products but only pure CO2.However, most fossil fuels are contaminated, especially in case of lignite, and thus thereis a large amount of water and other by-products produced during the burning, limitingthe heat generation and rendering it hard to control. Of all fossil fuels, natural gas is theeasiest to purify, and therefore it is, after purification, the most efficient and easiest tocontrol fossil fuel energy source.

1.1.2 Nuclear Power

Nuclear power is generated during the fission of Uranium (U). Uranium is a metal whichexists only as radioactive isotopes and only in mineral compounds. Albeit it is globallyrelatively abundant, it only exists in very few places in concentrations high enough tomine the ore. The most abundant isotope is 238U, which accounts for about 99%, whilethe second most isotope is 235U with an abundance of about 0.7%. The latter is, besidesthe Plutonium isotope 239Pu which is very rare, the only atom that is fissile in a selfsustaining chain reaction.

In nuclear power plants, 235U is used to generate energy: If 235U absorbs a free neutron,it turns into an excited 236U isotope which spontaneously decays into one of several pos-sible fission products and releases a large amount of energy in addition to three new freeneutrons. One common fission reaction is:

235U + n→236 U →141 Ba+92 Kr + 3n+ 210MeV.

The free neutrons that are produced in the fission process are very highly energetic andneed to be slowed down to increase the cross section to sustain the chain reaction. Thiscan be achieved either by using heavy water or carbon rods, depending on the type ofpower plant.

The fission process releases a lot of different waste products. First, there is a largeamount of highly radioactive waste from the decay products of the fission process that,by themselves, will only slowly decay through α- or β-decay processes, with half-live

3

1 Introduction

times that can be 10000 years or more. In addition, the highly energetic neutrons thatare produced during the fission process partially leave the chain reaction and render thesurrounding material radioactive. Therefore, there is not only the main waste from thefuel rods that needs to be stored, but also the shielding material around the reactor forwhich a storage-solution needs to be found. Therefore, this energy source leads to a long-lasting radioactive pollution for which, at the current state, no final storage or recyclingsolutions exist.

1.1.3 Climate Change

The historical climate of planet Earth can be measured over long geological timescales,using different tracers. While historical descriptions of human history are very vaguesources, and instrumental measurements have only been reliable over a few centuries,the climate record hidden in nature sources reaches back far longer. The best knownsource of such records are tree rings, which can cover timespans of up to 10000 years intothe past. For records dating even longer into the past, two major sources are used bygeologists: Ice cores from glaciers, the Antarctic, and the Arctic, and ocean sedimentsfrom all around the world. These sources date back to several hundred thousand yearsand millions of years, respectively, and contain climate proxies such as pollen, differentchemical isotopes or greenhouse gas imprints (see [5] for more details). These proxiesallow to draw conclusions about the temperature and the CO2 content of Earth and itsatmosphere.

Naturally occurring fluctuations of historical CO2 levels and temperature of the Earth’satmosphere due to tectonic processes, Earth orbital changes and changes in the strengthof the solar radiation can be observed on all timescales of the Earth’s lifespan. Thesechanges caused large changes in Earth’s climate, including four major ice ages over thelast 400 thousand years (see left panel of Fig. 1.2). During an ice age, the global averagetemperature is up to 8◦C below the current value. This is correlated with a drop of theCO2 level in the atmosphere from the historic maximum of a concentration of around300 ppm to 180 ppm, a change by 120 ppm. After the last ice age, which ended around 15thousand years ago, the CO2 concentration again rose by 120 ppm to the pre-industrialvalue of around 280 ppm on this relatively short timescale of several thousand years. Thisis a typical behaviour, similar to the behaviour seen after all ice ages. This provides abasis for a comparison with the effect human activity had on the atmospheric CO2 leveldue to the industrial revolution and the following large-scale combustion of fossil fuels thatreleased large amount of CO2 which was stored in the Earth’s crust for millions of years.

In the last 50 years alone, the CO2 concentration increased from 310 ppm in 1960 tomore than 400 ppm in 2017, already an increase by 90 ppm as shown in the right panel ofFig. 1.2. This will very likely lead to a significant rise in the global average temperaturedue to the greenhouse effect that is strongly driven by the concentration of CO2 in theEarth’s atmosphere.

The sun emits black-body radiation according to its temperature of about 5000 K, thatcorresponds to radiation in a wavelength range of about 300-1500 nm, fully covering thevisible light window (e.g. [7, p. 28]). Earth’s atmosphere is permeable for radiation inmost of this wavelength range, and thus a large portion of the suns energy can warm upthe planet. However, the planet reflects a large amount of this radiation and scatters itback to outer space, effectively cooling the planet down again. Due to the composition of

4

1.1 Conventional Energy Sources: Limitation of availability and climate change

Figure 1.2: Left panel: Amount of carbon dioxide in the Earth’s atmosphere in the last 400thousand years, measured through ice cores. Image credit: NASA. Right panel: Average globalcarbon dioxide concentration increase in the Earth’s atmosphere in the last 60 years, measured bythe Mauna Loa Observatory, Hawaii [6]. Image credit: NOAA/ESRL.

Earth and its atmosphere, this emission occurs in the infra red wavebands, where Earth’satmosphere is partly permeable as well (see Fig. 1.3). This cycle of heating and coolinghas been fluctuating over the lifetime of Earth as it strongly depends on the atmosphericmixture and the reflecting material on Earth’s surface (for example ice shields and waterareas).

Greenhouse gases can trap energy in Earth’s atmosphere by transmitting downgoingsolar radiation with short wavelengths but absorbing and reflecting upgoing thermal radi-ation at longer wavelengths. The most prominent and important greenhouse gas is watervapour which absorbs radiation in broad bands at both the short- and the long wavelengthends of the infra-red emission spectrum, as Fig. 1.3 shows. Due to the abundance of waterin the atmosphere, this absorption is very effective with a 100% saturation rate of theabsorption lines. Therefore the atmosphere only remains transparent to thermal radiationin a relatively small band around 10µm where the peak of the thermal spectrum is locatedthat contains a large fraction of its energy. Other greenhouse gases like especially CO2 andmethane now exactly absorb energy in wavelength around 10µm, and therefore close thisatmospheric transmission window. This effectively leads to an increase in Earth’s globaltemperature, as the thermal energy is trapped and cannot be radiated away any more. Atthe moment, these greenhouse gases are only present in trace amounts and the resultingabsorption is far from saturated, and thus an increase in their concentration has a strongimpact on Earth’s global warming.

As a consequence of this so-called greenhouse effect, the global warming is the mostlikely reason for the melting of the ice shelfs like the Larsen-C-Shelf (e.g. [8]), the decreasein the yearly extend of the Arctic ice shelf ([9]) or the increasing probability of extremeweather conditions like hurricanes. Therefore, it is important to reduce the human-madeCO2 emissions as quickly as possible.

5

1 Introduction

Figure 1.3: Atmospheric transmission windows and the impact of water vapour, carbon dioxideand other greenhouse gases on these windows: The uppermost panel shows the wavelength bandsat which the solar radiation passes the atmosphere and thus heats the planet in red, while thewavelength area in which Earth can emit heat through the atmosphere is shown in blue. Thesecond panel shows the wavelength windows of the atmosphere which are not blocked by absorptionor scattering through different molecules. For the most important molecule types that cause thisblocking, their respective scatterings and absorption windows are shown in the lower panels. Imagecredit: Wikipedia

6

1.2 Renewable Energy Sources

Global installierte Leistung der erneuerbaren Energien, 2015

in GW

0

100

200

300

400

500

600

700

800

SpanienItalienIndienJapanDeutschlandUSAChinaBRICSEU-28Welt

9242 36 33 32

122199

262276

784

Windkraft Photovoltaik Biomasse Geothermie Solarthermische KW

Quelle: Global Status Report (REN21 2016). Abweichungen zu deutschen Datenquellen beruhen auf unterschiedlicher Datenherkunft und Erhebungsmethodik. Abbildung ohne Darstellung der Wasserkraft. BRICS-Staaten: Brasilien, Russland, Indien, China und Südafrika

Figure 1.4: Global power of renewable energy sources in GW/h in 2015 worldwide (left), withinEurope (second left bar), and for individual countries with the largest contribution to this powerbudget. One of the major contributions comes from the combined approach of the Europeancountries, highlighting the need for a continental scale European solution for energy generation.Image credit: BMWi


Within Europe, the currently most important renewable energy source is hydro electricpower generation. Norway already produces 97% of its energy from hydro power, andIceland covers 100% of its energy demand from hydro and geothermal power generation.Outside Europe, hydro electric power also is one of the major renewable energy sources,and some countries like Costa Rica (93%), Brazil (76%), and Canada (62%) already usethis source of energy to generate large shares of their energy demand (e.g. [10]).

However, other sources like wind, solar energy and biomass have gained increasing im-portance even worldwide. From all countries worldwide, the European countries togetherhave the largest installed capacity of these renewable generators (see Fig. 1.4), clearlyhighlighting the need for a continental scale European energy network approach to fullyuse the existing resources and even expand the energy produced within the renewableenergy framework.

Solving large scale interconnectivity problems are not only important in between coun-tries, but also have to be addressed in large countries like China or the US. Both countrieshave relatively large installed capacities of renewable generators (see Fig. 1.4), requiringan optimized energy transmission network and storage systems (e.g. [11, 12] for a studyon the Chinese network system and [13] for a study about the optimal expansion of a USrenewable energy system).

One of the major concerns that arise for the integration of renewable energies into theenergy mix originates from their temporal fluctuations due to weather conditions andseasonal restrictions. Furthermore, their availability strongly depends on geographical

7

1 Introduction

features and thus not every region is suited for every kind of renewable energy production.In the following the different renewable energy sources and their dependencies will bediscussed in detail.

1.2.1 Wind Energy

Wind energy was already used for several centuries to power wind mills for mechanicalapplications, but their adaptation as electricity generators on utility scale only began inthe last two decades. Wind turbines use the kinetic energy of wind to rotate a set ofaerofoils and thereby drive an electrical generator. The power output of modern windturbines rises as a function of the wind speed v proportional to v3 (the kinetic energyof wind is proportional to v2 and the airflow across the rotor area yields another factorof v) until it reaches the rated power capacity. At larger wind speeds, the power outputis designed to remain constant at this level until the turbine has to be shut off to avoidstructural damage at very high wind speeds by rotating it out of the wind or reducing thewind angle of attack on the blades.

The wind speed increases with distance to the ground and with decreasing surfaceroughness due to the reduction of friction with the ground. Therefore, wind turbineswith increasing hub height and rotor diameter are developed to increase their efficiency.The surface roughness of open water is very low and wind speeds are often higher andmore constant than on land, and therefore off-shore wind turbines are more efficient inproducing energy but are more difficult and expensive to access, construct, and maintain.Wind turbines both on- and off-shore are often build together in large wind farms with alarge number of turbines to optimally exploit areas of good wind conditions and minimizeinfrastructure costs.

The worldwide potential for wind energy production is estimated by the InternationalPanel on Climate Change (IPCC) as (70 – 450) EJ/yr of realistic usable capacity [14],which considers not only technical but also economical and socio-economical constraints.Compared to the average worldwide energy demand of 393 EJ/yr (in 2015, [15]), underoptimal usage the available wind energy capacity is large enough to cover the worldwideenergy demand. According to Ref. [16], who estimate the realistic worldwide wind energypotential to be (1300 – 2700) EJ/yr, the available wind energy would even be one orderof magnitude larger than the worldwide energy demand.

Fig. 1.5 shows the distribution of the average wind power generation potential in Europe,both on land and off-shore, assuming typical wind turbines. The areas with the highestaverage wind speeds are located on and close to the North See and the Baltic Sea, especiallyin and off of Ireland, Great Britain, and Denmark, where a typical wind turbine canproduce power at rated capacity for almost half of the time per year on average.

Wind energy availability is mostly coupled to weather patterns. In Europe, the majordriver of weather patterns are Rossby waves [17]. They are a turbulent phenomenon ofthe atmosphere driven by a north-south temperature gradient on a rotating sphere. Thesewaves lead to a mixing of cold polar air and warm subtropical air, and form large-scalepockets of constant air pressure of sizes of 600–1000 km, and are usually stable for 3–10days and thus determine the synoptic weather patterns. Therefore, this is the dominanttimescale on which wind energy production fluctuates in Europe. As the Rossby wavesfluctuate seasonally in strength, this causes an additional seasonal timescale for the windenergy production, leading to a generally stronger wind energy output in the winter.

8


0.08

0.16

0.24

0.32

0.40

0.48

0.56

0.64

wind

ave

rage

cap

acity

factor

Figure 1.5: Distribution of the average wind power generation potential in Europe, both on landand off-shore, assuming typical wind turbines. The highest production rates of energy from windturbines are shown in red, and can reach more than 60% capacity utilization.

1.2.2 Solar Energy

Solar radiation provides almost all of the energy needed to sustain life on Earth. Itallowed the animals and plants, which were later transformed into fossil fuel, to grow, butalso drives the atmospheric turbulence that can be used to generate wind power. Solarirradiation can also be used more directly to produce electricity in solar photovoltaic(PV) panels. They generate electricity via the quantum mechanical photovoltaic effect,in which a photon with sufficient energy, usually from the visible part of the spectrum, isabsorbed in a semiconductor. It thereby excites a valence electron over the band gap tothe conduction band. A special structure of the semiconductor, a p-n-junction, creates anelectrical field that allows the electrons to pass only in one direction and thus collects theexcited electrons at one end of the solar cell, thereby creating an electrical current.

Solar PV panels require direct or indirect sunlight to generate electricity. They producemore energy with higher irradiation density and longer average irradiation duration, andare therefore most efficient in southern European countries, especially in Spain and Italy(see Fig. 1.6). The worldwide solar energy generation potential is estimated to be around(1300 – 15000EJ/yr [18], which would be more than three times the global energy demand,however, the production is strongly concentrated at the equatorial regions and thus theworldwide energy distribution is difficult. In Europe, the highest production rates are onlyat 20% capacity utilization due to the diurnal availability, cloudiness and the inefficiencyof the currently available solar panel technology.

The highest energy production rate for a solar panel is achieved if it is oriented per-manently towards the sun. However, this would require mechanical tracking of the solarposition, which is often too expensive and introduces moving parts into the panel design

9

1 Introduction

0.08

0.10

0.12

0.14

0.16

0.18

0.20

solar a

verage

cap

acity

factor

Figure 1.6: Distribution of the average solar power generation potential in Europe, assumingtypical solar panels. The highest production rates of energy from solar panels are shown in red, andreach about 20% capacity utilization due to the diurnal availability, cloudiness and the inefficiencyof the currently available solar panel technology.

which can break down and require maintenance. Therefore, solar panels are usually buildsouth-facing with tilt angles corresponding to geographical latitude to maximize the aver-age annual irradiation intensity and duration. Most commonly, solar panels are installedon south- or east-facing rooftops or facades of buildings, or in large-scale arrays of panelson open areas. However, there they can conflict with other forms of landuse like agricul-ture. Additionally, solar panels are manufactured mostly from silicate but also requirerelatively rare elements, some of which are toxic. This makes it problematic to dispose ofold panels, but specialized recycling techniques can extract these elements, which allowsto reuse them and reduces the health hazards, albeit they are cost- and energy intensive.

Another technology option that directly uses sunlight is solar thermal power generation.Here, the solar radiation is concentrated into a small volume via large arrays of parabolicmirrors in order to generate heat that can drive a conventional electric generator. Theheat can also be stored temporarily, e.g. by melting sand, which allows to continue energygeneration during the night, however this technology requires non-scattered, direct sunlightfor extended periods of time and is therefore restricted in Europe to desert-like regions inSpain.

Since no sunlight is available during the night, solar energy generation has a strongday/night variability. There is also a seasonal variation pattern of higher irradiationdensity in the summer than in winter that is due to the tilt of the Earth’s rotation axisrelative to the sun and the resulting change of the influx angle on the surface of the Earth.Additional fluctuations are driven by the cloudiness, which is a more localized phenomenonand does not follow a clear weather pattern like the wind distribution. Therefore, these

10


0.00

0.03

0.06

0.09

0.12

0.15

0.18

0.21

0.24

0.27

Surfa

ce ru

noff [kg/m

2/h]

Figure 1.7: Distribution of the surface runoff in Europe that can be used for hydro power gener-ation. The highest runoff rates are shown in red, and reach about 0.2 kg/m2/h.

fluctuations are relatively short-lived and thus the synoptic timescale is the least importanttimescale with respect to solar energy production.

1.2.3 Hydro Power Energy

Hydroelectric power plants use the kinetic and potential energy of rivers by channellingthe water through a turbine to generate electricity. Prior to the 20th century it was mostlyused to power or grain mills or forges, but with the advent of electric power grids it becamethe most common source of renewable energy.

In run-of-river power plants the kinetic energy of a large river is used and thereforeits generated power depends on the flow rate which might vary over time. These plantsare usually dimensioned such that turbines can run at full power most of the time, i.e.,a significant amount of water is spilled when the inflow is large. This allows a constantenergy generation and reduces the impact on the flora and fauna.

Water can also be retained behind large storage dams if the geological conditions inthe upstream region are suitable, for example in mountainous regions with tight canyonsor in fjords. The amount of generated power can then be controlled even on very shorttimescales as long as there is enough water in the storage. Some storage reservoirs, e.g. inNorway, are large enough to retain most of the annual inflow, allowing to shift generationon a seasonal timescale over several months. They can also dispatch power almost instantlywhen needed, and thus provide a large amount of reliable short and long term flexibilityto the system.

Both kinds of hydroelectric power plants require water inflow to drive the turbines orto fill the reservoir lakes. Flow rates in rivers depend on precipitation or snow melt in

11

1 Introduction

spring, and therefore have a seasonal variability, however, the storage dams can compen-sate for this and smooth the seasonal fluctuations. In Europe, precipitation is highest inmountainous regions such as the Alps and the Norwegian fjords, where humid air is forcedto rise upward, cools, and begins to precipitate. Therefore, the surface runoff that collectsthis rain water and the potential for hydro power generation is highest there as well, seeFig. 1.7.

However, since hydro electricity is a very clean and, after the initial construction, alsocheap source of energy, most suitable locations in Europe are already in use nowadays.Additional installations are unlikely due to environmental and socio-economic concernsthat arise with the permanent flooding of large valleys which is necessary for constructingnew hydro dams.

As an alternative to generation of energy through flowing rivers, hydro power can alsobe gained from tidal forces at the ocean shores. Driven by the gravitational force of themoon, large bodies of water are pulled from the costs to the open sea and are pushedback every 12 hours. To use the energy from tides, generators can be installed in coastalareas with large tide heights, where ebb and flood alternately push water through theturbines in two different directions, generating electricity both ways. The oldest suchpower plant was build in France in 1966, has an installed capacity of 240 MW, and is thesecond-largest tidal power plant in the world. It is currently also the only tidal power plantinstalled in Europe (see [19] for more details). As current technologies need a relativelylarge tidal range in height and the construction of these plants is still very expensive, thereare currently no indications for a possible large-scale implementation, which is why thistechnology is not considered further in this work.

1.2.4 Biomass

Biomass as a fuel source is the oldest form of renewable energy source and has mostlybeen used in form of wood pellets since thousands of years. It can be used in two differentways, namely either directly burned or transformed into other forms of fuel: Biomass canbe thermally processed to gain charcoal, chemically processed into biodiesel, or fermentedinto bioethanol. Biodiesel and bioethanol are attractive due to their high energy densityas possible fuel in the current transport sector (e.g., for trucks, air planes, and ships).Currently, common sources of biomass are energy crops, forestry residue, manure, andorganic waste. In 2015, biomass was the fourth most-important source of renewable energyworldwide (see also Fig. 1.4). In Europe, biomass electricity contributed 104 TWh/yr,which corresponds to 3.8% of the electric energy consumption [20].

As biomass is theoretically CO2 emission free and dispatchable, it is in principle con-sidered to be environmentally friendly. However, a life-cycle analysis of biofuels showsa potentially low energy efficiency and significant CO2 emissions that originate from thecultivation of energy crops, especially through the use of fertilizers which are energy inten-sive and produced through CO2 emitting methods [21]. Additionally, the whole logisticalprocess from harvest over transportation to the final processing of the biomass into fuelis CO2 intensive, and thus counteracts the environmental neutrality in CO2 emission bal-ance. Furthermore, the total energy potential of biomass is limited as most of the landuse is needed for food agriculture, and energy crops especially deprive the soil of nutrients,which increases the need for fertilizers. Many types of organic waste material could also beused for other purposes for example as natural fertilizers. Therefore, biomass is excluded

12

1.3 Energy Storage Options

from the analysis provided in this work, as its CO2 emission balance is under debate andthus a conservative estimate of a possible highly renewable energy network is chosen forthis study.

1.3 Energy Storage Options

In an energy mix that is dominated by renewable energy sources that are strongly fluctu-ating in energy output, one of the most important ingredients is the existence of storagesystem. These systems can store energy at production peak times, if the energy productionexceeds the demand, and release this energy in underproduction periods. Several differentstorage options currently exist. However, all of them suffer from different restrictions, andno optimal storage possibility is found yet.

1.3.1 Pumped Storage Hydro Power Stations

Pumped hydro storage is a technologically fairly simple method of storing energy. Ituses the height difference between two water reservoirs to store energy: Water is pumpedup to the higher level reservoir using the overproduced energy, thus storing this energyas potential energy at the higher ground level. Once the energy is needed, the water isreleased into the lower reservoir, thereby flowing through turbines which “re-generate” thestored energy into electricity.

This storage method has a high round-trip efficiency and is highly flexible as it canreverse the operation direction within a few minutes. Similar to the hydro power plants,pumped hydro storage is only expensive in the building process, but afterwards it is cheapto maintain and operate. On the downside, this storage method has strong geologicalrequirements, as it needs two reservoir basins in close proximity with a large height differ-ence. Similar to the situation that has been described for hydro power plants, the availablespace to install such hydro storage facilities is limited and already fully utilized in Europe.

1.3.2 Batteries

Batteries are commonly used for many purposes, and are implemented in the energystorage network as well. Different battery electricity storage technologies are available,which are all based on reversible electrochemical reactions. One of the most relevantbattery technologies are lithium-ion-batteries. They are an already proven technologyused in many electronic devices, and increasingly for battery electric vehicles (and homestorage systems), where costs are falling rapidly due to cell manufacturing improvementsand economy of scale effects [22]. Thus, this technology is expected to grow in importanceand replace other, currently more common forms of storage for large scale applications,such as lead-acid batteries.

Lithium-Ion-batteries store energy through a chemical process where lithium ions aretransported between anode and cathode through a semi-permeable membrane and par-ticipate in different electrochemical reactions at both sides, storing energy in the electro-chemical potential of the resulting compounds. Lead-acid batteries operate with a similarapproach with different electro-chemistry, however, lead is a highly toxic substance andthus a less toxic alternative is desirable.

13

1 Introduction

Batteries are extremely flexible and can react at or below the timescale of seconds, andare therefore already used to provide storage and flexibility in isolated, 100% renewablesolar–battery island grids (e.g. [23]). In Europe, they are increasingly used in local andoff-grid systems and are expected to be deployed on a large scale as installations of variablerenewables continue to increase [24].

1.3.3 Hydrogen storage

Energy can also be stored in the chemical potential of molecular hydrogen (H2) producedvia the electrolysis of water. In this process, an electrical current provides enough energyto dissolve the molecular bonds of water molecules, creating hydrogen and oxygen. This isa well known chemical reaction discovered already in the 19th century. The energy storedin this chemical process can easily be restored to the system by reversing this process,i.e., oxidizing the hydrogen to form water, which is the only waste product of this process.The reverse process has on gigawatt scales already been commercialized in form of fuelcells, with 480 MW installed already in 2016 [25]. This storage process operates veryflexible as well, albeit slightly slower and less efficient than the battery storage system.An advantage over batteries is that the hydrogen gas can easily and cost-efficiently bestored in steel tanks in large quantities and therefore can have a large enough energycapacity to provide long-term storage at relatively low cost. However, hydrogen storagehas not yet been used on a large scale due to high total cost and relatively low efficiency.

While hydrogen storage is currently discussed as a method to store energy from overpro-duction in renewable systems, the hydrogen produced in this process is a valuable energycarrier in itself that can be used for different purposes. It can directly be used as fuelfor hydrogen cars, albeit this would require the build-up of a hydrogen infrastructure torefuel the cars. Alternatively, hydrogen can also be used for methanation, where it canbe combined with CO2 to synthesise methane, which can be used as fuel for air planes ortrucks as it has a high energy density.

Electrolysis was commercialized already at the megawatt scale to obtain hydrogen [26].Currently, the most common way for industrial hydrogen production is to dissolve methaneinto hydrogen and CO2, but this method is not suitable for highly renewable energysystems as it consumes fossil fuel and directly produces CO2 in the reaction. Thus, usingwater for electrolysis is a much cleaner solution to obtain hydrogen, either for storage orother purposes.

1.4 In this work

This study discusses the flexibility requirements of a European energy network and itscost efficiency in dependence of the fraction of renewable energy sources and storage ca-pacity integrated in the network. Based on the energy sources discussed in this chapter,a simplified model of the European energy network is introduced in Chap. 2 to analysethe flexibility required on different timescales in a highly renewable electricity system. InChap. 3, this model is extended to include storage systems, and the influence of the stor-age on the flexibility requirements is examined. Interconnecting transmission and hydroelectricity are added to the model in Chap. 4 to study the properties of a cost optimalhighly renewable energy solution for Europe and the benefit of cooperation between theEuropean countries. Finally, in Chap. 5 a sensitivity analysis is provided to explore the

14

1.4 In this work

impact of policy restrictions and changes of economic assumptions on the model. Chap. 6provides a summary of the results presented in this study together with a final conclusionand an outlook for future work.

15

2 Integrating Renewables with BackupFlexibility Classes1

2.1 Introduction

The dispatchable electricity generation facilities that are widespread today were mainlyconstructed with the aim of matching demand requirements. They split more or less intothree flexibility classes, which are able to follow the typical load variations on the intra-day, intra-week, and seasonal timescales; see Fig. 2.1. During the day, variations in theload are usually due to human activity. Furthermore, the load is reduced during weekendsand public holidays, and seasonal changes lead to higher load in the winter due to longernights and increased heating demand. Examples of current slowly flexible generators arenuclear and lignite power plants, coal and combined-cycle gas power plants are mediumflexible, and open-cycle gas turbines are highly flexible.

This mix of conventional power generation plants is going to change. In order to mitigatethe negative impact of climate change, some countries (like Germany and Denmark) arefollowing ambitious targets on reducing CO2 emissions and on increasing the integrationof renewable energies [29]. Both targets pressure the existence of some of the conventionalpower plants, in particular the lignite and coal power plants. As to the second target, theincreasing share of weather-driven variable renewable energy sources (VRES) – mainlywind and solar PV power – poses new challenges, and in particular leads to an increase influctuations of the residual load. This requires more highly flexible backup power plants.Slowly flexible power plants will be less needed, but phasing them out too early mightturn out to be a mistake.

In highly renewable electricity systems the same three flexibility timescales as in theconventional power systems are also present [28]. They are determined by the weathervariations which cause the wind and solar power generation to fluctuate. The intra-day timescale is called the diurnal timescale and is most clearly seen in the solar powergeneration following the availability of sunlight; see again Fig. 2.1. Wind variations aredominated by synoptic weather patterns in Europe, which fluctuate on the timescale ofthree to ten days [30]. These weekly fluctuations also have an effect on the solar irradiationand thus the solar photovoltaic (PV) production. Finally, seasonal changes are observed,with typically more wind power production and less solar PV generation in winter andvice versa in summer.

To include a large share of variable renewable energy, the energy system has to becomemore flexible. There is a considerable spread in the interpretation of what flexibilityin the electricity system actually means, ranging from the more direct definition of theability to react to variability, e.g. [31], and uncertainty of forecasts of variable generation[32], to more indirect policy, regulation, and market implementation issues of making

1This chapter has been published as Schlachtberger et al. (2016) [27] and was only slightly modified forthis work.

17

2 Integrating Renewables with Backup Flexibility Classes

2000

2001

2002

2003

2004

2005

2006

2007

0.0

0.5

1.0

1.5

2.0

2.5

Power / <L>

(a)

Load (mo) Wind (mo) Solar (mo)

Wed Fri Su

nTue Th

u SatMo

nWe

d0.0

0.5

1.0

1.5

2.0

2.5

Power / <L>

(b)

Load (h) Wind (h) Solar (h)

Figure 2.1: Examples of time series of load and weather-based wind/solar generation in Germanybased on data described by [28]. (a): All eight years of data, smoothed over one month to seelong-term trends. (b): Hourly load and generation for two example weeks in October 2000. Alltime series have been normalized to an average load of one.

balancing energy and power available, e.g. [33]. Depending on the complexity of themodelled system, different flexibility metrics have been proposed or reviewed. Metricsbased purely on the properties of the residual load at given shares of variable generation aredefined by [34]. They allow insight into principal properties of the flexibility requirementsof the dispatchable part of an energy system. In a similar setting, [35] focus on flexibilityneeds based on (residual) load gradients over different time intervals and spatial scales inEurope. Additional metrics can be defined in dispatch simulations, e.g. to measure thedifference between forecast and actual (residual) load [36], missing or surplus energy, ormissing or surplus power [37] (see [38] for a comprehensive summary). These also includedifferent metrics for the (in-) sufficiency of flexibility in the systems, such as the loss ofload expectation or the number of unserved hours [36]. This study concentrates on thechallenges posed by ramp rates in the residual load, measuring the quality of the flexiblesystem in terms of unserved energy.

Dispatchable generators are not the only possible source of flexibility. Recent stud-ies considered the influence of storage (e.g., [39]), transmission grid extension (e.g.,[40]),demand-side-management, curtailment, system integration with the heating (e.g.,[41]) andtransport sector (e.g., [42]), economic efficiency (e.g.,[43]), forecast errors, and combina-tions thereof. [44] provide a thorough review of different technical, economic, and marketbased modelling approaches and requirements for the different aspects of flexibility de-mand. A range of more specialized flexibility metrics for these options is reviewed by[45].

This chapter analyses a stylized model of the European electricity system, consisting ofweather-based wind and solar PV generation and historical load data from Ref. [28] withhourly resolution. These are assumed to be complemented by dispatchable generation ofthree flexibility classes, which are designed to follow the load and the renewable powergeneration on the diurnal, synoptic, and seasonal timescales, respectively. To define thethree flexibility classes, maximum ramp rates are assigned in a top-down manner. Theirtotal capacities as well as their dispatch are treated as optimization variables. Similarflexibility classes are also defined in Ref. [46], where a Fourier-like decomposition of the

18

2.2 Methods

residual load is used to estimate flexibility requirements, but their model focuses on aoptimal decommissioning of the currently installed capacities.

First discussions of the explicit impact of the dominant meteorological timescales onthe required backup infrastructure of highly renewable large-scale electricity systems haverecently been put forward. [28] discuss a seasonal optimal mix of wind and solar power,where the combined renewable power generation exactly follows the seasonal dependenceof the load. They find that this greatly reduces the need for storage. In addition, [47] showthat the remaining required amount of storage is mainly determined by the fluctuationsof the renewable power generation on the synoptic timescale. With the same modellingapproach, [48] and [49] estimate the transmission needs across a highly renewable Europeanpower system, highlighting the importance of large-scale transmission grid expansion. Thebalancing energy and power requirements have been addressed in [50] and [51]. However,all the balancing needs have been assumed to be only highly flexible. Different flexibilityclasses have not been discussed there, and will be the main focus of this study.

The model presented here uses the backup system as only source of flexibility. Thissimplified approach allows to assess the general trends of the flexibility requirements, andespecially the optimal contribution of slowly flexible generators in the electricity sector if noother flexibility options are available. However, the model does not consider the impact ofadditional flexibility like storage and transmission to avoid the complex interplay betweendifferent flexibility options in more detailed models [44]. Nevertheless, it can be used toprovide a basis for the quantification of the benefits of other options.

The chapter is organized as follows: Sec. 2.2 describes the data base and the modellingapproach. Further technical details of the model can be found in 2.8. The main results arepresented in Sec. 2.3, whereas model sensitivities to the physical parameters are shown inSec. 2.4. The results as well as model assumptions and potential extensions are discussed inSec. 2.5. Sec. 2.6 compares the decommissioning timescales of the optimized and installedslowly flexible capacities in Germany. Finally, Sec. 2.7 summarizes the conclusions andprovides an outlook for further relevant research topics.

2.2 Methods

In this chapter the power system model consists of variable renewable energy generationfrom wind and solar PV in combination with a dispatchable, conventional backup systemthat together balance the electricity consumption.

2.2.1 Data

The power generation data for wind and solar energy are based on historical weatherdata for 30 European countries covering the years 2000 to 2007 with time resolution of1 h on a grid with a spatial resolution of about 50 × 50 km2, as described in detailby [28]. There, the generation data were aggregated on country level, ignoring nationaltransmission constraints. These authors also provided the corresponding national hourlyenergy consumption data as published by the transmission system operators [52]. Here, thetime series for wind power generation W (t), solar power generation S(t), and consumptionL(t), are normalized to their mean 〈W 〉 = 〈S〉 = 〈L〉 = 1, where 〈·〉 is the time average ofa series.

19


Whenever the consumption is higher than the renewable generation, the remainingdemand has to be covered by a backup system. This residual load LR(t) at each hourt is calculated as the positive part of the difference between consumption and renewableenergy production:

LR(t) = (L(t)− γ [αW (t) + (1− α)S(t)])+ (2.1)

where α ∈ [0, 1] is the wind fraction in the relative share between wind and solar powergeneration, and γ is the VRES gross share, i.e. the average combined wind and solarpower production in units of the mean load. For γ = 1, the average renewable generationequals the average consumption over the 8-year period. Here, (X)+ = max(0, X) denotesthe positive part of a quantity X. Similarly, (X)− = −min(X, 0) is the negative part ofX.

Throughout this chapter, a fixed wind-solar ratio of α = 0.7 is chosen for each country,which is a good approximation to the optimal mix that minimizes the average residualload [48].

2.2.2 Modelling dispatchables

The electricity system beyond load and VRES generation is modelled in a simplified fash-ion. It is assumed that VRES take precedence in covering the demand. Whenever VRESoverproduction occurs, it is assumed to be curtailed. The residual load (cf. Eq. 2.1)is covered by a dispatchable backup system in order to guarantee the security of sup-ply. Storage is not included at this point. Working with country-aggregated time series,country-internal transmission bottlenecks are implicitly neglected. Only two limiting casesof power transmission are regarded: isolated countries, corresponding to zero cross-bordertransmission, or aggregated Europe, corresponding to unconstrained transmission. Thesecases provide bounds for a more detailed system with partly congested international trans-mission. The two reference cases here are Germany without international transmission andan aggregated Europe.

In order to study the flexibility requirements in more detail, the backup system is splitinto three flexibility classes, based on the timescales of the variations they cover. As seenin Fig. 2.1, the variations of load and renewable generation typically occur on the intra-day, synoptic, and seasonal timescales. The flexibility classes are therefore implementedinto the model by splitting the dispatchable system into a daily, a synoptic, and a seasonalpart. For each of these parts i, the maximum rate of change mi of their power outputBi is limited. As the seasonally flexible part is the slowest and the daily flexible part thefastest, the three systems are also referred to as the fast, the medium, and the slow system.Furthermore, the power capacities of the three components are limited to Ki. Together,the dispatch of the three components is optimized in a way that minimizes excess anddeficit of backup energy with small installed capacities and high utilization.

20

2.2 Methods

This is done by solving the optimization problem:

min Φ =

[∑t

(LR(t)−

∑i

Bi(t)

)2

︸︷︷︸match residual load closely

+ c∑i

wiKi︸︷︷︸reduce power capacities

+d

T

∑i,t

viBi(t)︸︷︷︸increase utilization

] (2.2)

subject to

∣∣∣∣∆Bi(t)∆t

∣∣∣∣ ≤ mi,

0 ≤ Bi(t) ≤ Ki,

with i = fast,medium, slow; t = 1, . . . , T

where t runs over all T = 70128 hours of the 8 year time series. The parameters c, wi inthe second term are the relative weights of the capacities, with priority given to the lessflexible classes. The latter is necessary to avoid the trivial optimum where only the mostflexible system is used to perfectly match the demand. The last term determines the orderin which the three systems are dispatched, via the weights d, vi with which the usage ofpotential backup energy production of class i is encouraged, leading to higher utilizationof slower systems.

Parameter choices

Ramp rates A lower bound on the ramp rates present in the current system can beinferred from the load data. The contribution of renewables in the years 2000–2007 wasvery low (γ ≈ 0 [49]), and the conventional dispatchable power system thus covered thefull load almost on its own. Therefore, the ramp rates mi of the historic dispatch can beextracted from the load in the following way:

1. The maximum ramp rate mslow of the slow system is set to the maximum slopeof the load over the relevant timescale of one week. Before calculating the slopes,fluctuations on shorter timescales are suppressed by smoothing the load time seriesvia convolution with a Gaussian kernel Kerτ (t) =

√π/(2τ2) exp(−π2t2/(2τ2)) with

a standard deviation of one week (τ = 168h), which replaces each load value by aweighted average of its neighbours. Therefore, mslow = max(| ddt(Kerτ ∗L)|), where Lis the load time series, f ∗g is the convolution of f and g, and |·| is the (element-wise)absolute function.

2. The maximum ramp rates mmedium of the weekly variations are then calculated ina similar way. To avoid contributions from variations on the longer timescales, theweekly smoothed load time series is subtracted from the load first, then only theremainder is convolved with a Gaussian of the width of one day (τ = 24h).

3. The fastest components are assumed to be flexible enough to follow the slope of theload at all times and therefore mfast remains unconstrained.

21


Table 2.1: Parameters of the reference models Germany (DE) and aggregated Europe (Agg).

class mi[% 〈L〉 h−1] wi vi c dDE Agg.

fast unlimited unlimited 1 1 40 0.1medium 2.26 1.34 0.5 0.5 40 0.1slow 0.25 0.17 0.25 0.25 40 0.1

The ramp rates are calculated from the load of each country separately, or in the aggregatedcase from the aggregated load over all countries. The mi of the reference models are listedin Table 2.1. The given mmedium correspond to 54% / 32% 〈L〉 day−1 for Germany /aggregated Europe, and the mslow to 42% / 29% 〈L〉week−1.

Even the least flexible power plants that are currently used for baseload production havetechnical constraints that allow them to change their power output, and even performa cold start on relatively short timescales of less than 1–24 hours. However, it is noteconomically and ecologically feasible to cycle typical baseload plants on a regular basis,as shown by [53] for a US case study and by [54] for a German market. It is thereforereasonable to limit their ramp rates as an effective means of including these economic andregulatory constraints.

Capacity weights The only difference between the flexibility classes in the model is theirmaximum ramp rates. If the capacities were unconstrained, the fastest backup componentcould cover the load perfectly on its own without any need for the slower components. Toavoid this trivial optimum, the capacity weights are set to wfast > wmedium > wslow. Theweights wi used in the reference model are listed in Table 2.1. The model is found to berelatively insensitive to the ratio of these parameters as will be discussed in Sec. 2.4.3.

Dispatch weights In the reference scenario, the dispatch weights vi are increased withthe flexibility of the class as shown in Table 2.1, in order to increase the utilization of theslower systems, which generally require more full load hours to be economically feasible[53].

As a side effect, the degeneracy in the order of the dispatch at the hours when nocomponent is needed to its full capacity is lifted by the weights vi in the third term inEq. (2.2). The first two terms in the optimization function determine the total hourlydispatch and the capacities of the three system types, but they do not provide a uniquesolution for the distribution of the dispatch of the three components. With the inclusionof the third term, the slower systems are preferred. Avoiding the degeneracy requires onlya small weight for this term, and d = 0.1 was chosen as this was found in this study tobest reproduce the typical dispatch characteristics of today’s system.

Missing energy The objective function Eq. (2.2) does not require a perfect match be-tween demand and supply, but only aims at minimizing the uncovered load as well asexcess production by the dispatchable systems. In practice this residual mismatch couldbe covered by a limited amount of load shedding and additional curtailment of renewablegeneration, respectively, or other means of load shifting, depending on the economics ofthe various measures. Allowing a small deficit in energy production removes the otherwise

22

2.2 Methods

disproportionately large influence of a small amount of extreme load hours on the backupcapacities. In the model, the total amount of energy Emiss that is not covered duringthe full range of the time series depends mostly on the capacity of the fastest backupcomponent. The minimum amount of total covered energy was set to 99.97%, such that20 average load hours (av.l.h.) are allowed to remain unserved over the course of the eightyear time period. This can be done by setting the capacity weight cwfast = 40, as dis-cussed in the following. Emiss = 20 av.l.h. corresponds to full load coverage for about 99%of all hours at a renewable gross share of γ = 30%. The number of uncovered hours as afunction of γ is shown in 2.8.1.

Numerically, it is observed that the amount of missing energy can be controlled by theweights cwfast as:

Emiss =∑t

(LR(t)−

∑i

Bi(t)

)+

≈cwfast

2(2.3)

where Emiss is measured in units of the mean hourly load 〈L〉. This can be understoodby considering a variation of the optimization function with respect to the fast capacityKfast. One can assume that in an uncovered hour all backup capacities are operated veryclose to full capacity, such that

∑t

(LR(t)−

∑i

Bi(t)

)+

≈∑t

(LR(t)−

∑i

Ki

)+

(2.4)

If the fast capacity is too small, a given Emiss can only be achieved by increasing slowor medium generation, which leads to considerable overproduction. Therefore, the opti-mization mainly seeks a trade-off between reducing the amount of uncovered energy andincreasing the fast capacity. Denoting the optimization function by Φ and using the firstpart of (2.3), this trade-off can be approximated by

δΦ

δKfast≈ δ

δKfast

∑t

(LR(t)−

∑i

Ki

)2

+

+ c∑i

wiKi

= − 2Emiss + cwfast

!= 0

(2.5)

which yields the second part of (2.3).

In a similar way, the excess energy from the three flexible systems

Eexcess =∑t

(LR(t)−

∑i

Bi(t)

)−

(2.6)

is determined by the slow capacity. The optimization in this case seeks to reduce theamount of excess energy by lowering the use of slow capacity. But less slow capacity alsoincreases the amount of missing energy, since almost all of the capacity of the backupsystem is needed to cover the highest demands, as argued in the previous paragraph. Thevariation of Φ with respect to Kslow therefore influences both excess and missing energy,

23


although in opposing manner, and in analogy to (2.5) can be well approximated by

δΦ

−δKslow≈ 2Emiss − 2Eexcess − cwslow

!= 0 (2.7)

In combination with (2.3) this then yields

Eexcess =∑t

(LR(t)−

∑i

Bi(t)

)−

≈cwfast

2− cwslow

2(2.8)

which is also observed numerically as long as the weight d of the utilization term inEq. (2.2) is as small as in the reference model. Since both Emiss and Eexcess are onlyfunctions of the capacity weight parameters, they can be controlled independent of othermodel parameters like the maximum ramp rates or γ.

2.3 Results

2.3.1 Development of dispatchable capacities

The development of the optimal capacities of the modelled dispatchable backup systemsfor increasing gross shares γ of VRES is shown in Fig. 2.2 for Germany as an isolatedcountry. The total required backup capacity Ktot =

∑iKi (magenta line) does not de-

crease significantly from its initial value of Ktot = 1.35 in units of the mean load 〈L〉. Itdecreases only slightly to Ktot = 1.16 and 1.09 even for very high VRES gross shares γ = 1and 2, respectively. At γ = 0, the dominant share of the backup capacity is contributed bythe slowly flexible system (green line) with a capacity of Ks = 0.88. However, for largerγ Ks falls off significantly until it is below Ks < 0.2 for γ > 0.5. The capacity Km ofthe medium flexible class (red line) starts for γ = 0 at Km = 0.2, peaks to Km = 0.43at γ = 0.35, and drops below the initial value for γ > 1. The fast capacity (blue line) isalmost constant at Kf = 0.27 for γ < 0.2, but then rapidly increases towards Kf ≈ 0.9for γ > 1.

These results can be intuitively understood with the help of the modelled dispatch ofthe three flexibility classes shown in Fig. 2.3(a-c). All three panels show the same twoweek period as Fig. 2.1(b), but at three different levels of VRES shares with γ = 0, 0.5,and 1, respectively.

For γ = 0 the VRES do not contribute and the backup system has to cover the fullload. As the load varies only moderately around its mean in this case, the slowly flexiblesystem is able to cover a large fraction of it, as indicated in Fig. 2.3(a). The remainingload especially during the weekends is small enough to be covered mostly by the mediumsystem, while the fast system covers the fluctuations on shorter timescales. The slow andmedium flexible systems are often used to their full capacities, especially during the wintermonths when the consumption is highest, in accordance with the optimization objective,as discussed in Sec. 2.3.3.

In the case of γ = 0.5, the situation changes significantly, as shown in Fig. 2.3(b). Thehigh share of VRES leads to large fluctuations in the residual load. This includes hourswith virtually unchanged maximum load that require the full backup capacity, but alsohours with zero residual load when the VRES production is larger than the demand and has

24

2.3 Results

0.0 0.5 1.0 1.5 2.0

VRES gross share

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

dis

patc

h c

apaci

ties

/ <

L>

TotalDailySynopticSeasonal

Figure 2.2: Modelled optimal backup capacities in units of the mean load versus VRES grossshare γ for Germany. The blue, red, and green lines correspond to the fast, medium, and slowflexibility classes, respectively. The sum of the three capacities is given by the magenta line.

Wed 11

Fri 13

Sun 15

Tue 17

Thu 19

Sat 21

Mon 23

Wed 25

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Power / <L>

γ=0.0

(a)LR

DailySynopticSeasonal

Wed 11

Fri 13

Sun 15

Tue 17

Thu 19

Sat 21

Mon 23

Wed 25

Date in Oct 2000

γ=0.5 (b)

Wed 11

Fri 13

Sun 15

Tue 17

Thu 19

Sat 21

Mon 23

Wed 25

γ=1 (c)

Figure 2.3: A two-week period of the modelled dispatches for Germany for γ = 0, 0.5, 1 in panels(a,b,c), respectively. The dispatches of the slow, medium, and fast flexibility classes (green, red,blue lines) are plotted cumulatively, and together match the (residual) load (black lines, mostlyoverlapped by the blue lines) at almost all times.

25


to be curtailed. Due to the large share of wind power in the mix of the renewables, theseoverproduction events typically happen on a synoptic timescale. The medium flexibilityclass is therefore well suited to follow these fluctuations, leading to the increase in Km forrelatively small γ < 0.3 shown in Fig. 2.2.

However, for larger shares of VRES additional overproduction events occur on evenshorter timescales of hours to days, as indicated in Fig. 2.3(c). The medium system isthen no longer flexible enough to follow most of these fast variations and its capacitydecreases with γ as observed above. Kf is substantially increased as the fast system hasto cover the large remaining variations.

The trends of the capacities at different γ described above agree qualitatively with theresults reported by [34] for a case study of California’s electricity system. These authorsdefine comparable flexibility classes but use a purely statistical approach. They also find asharp decrease of Ks from 13% to 50% renewable penetration, a slightly peaked Kmedium,and an increase in Ks as function of γ. However, their model does not optimize capacitiesand results in a much smaller share of slow capacity in the initial system, compensated bya large share of fast capacity.

2.3.2 Aggregation benefits

In the previous section the case of an isolated German electricity system without trans-mission to other countries was discussed. Fig. 2.4 illustrates the benefits of unlimitedtransmission in an aggregated Europe, where excesses and residual loads are shared andexchanged. Here the total capacity decreases significantly with γ from 1.37 to 0.85 forγ = 0 to 1 and even further to 0.53 for a large over-installation of VRES with γ = 2. Thisis in contrast to the much slower decrease in the isolated case. Comparable benefits oflarge scale aggregation for the total required capacity and energy are also reported by e.g.[46].

In the aggregated case, Ks is higher by ≈ 0.1 〈L〉 for γ < 0.5. This is due to thesmoothing effect of spatial aggregation where opposing fluctuations in different regionscancel each other, leading to less extreme variations (see e.g. Ref. [35]). The smootherglobal residual load can therefore be better matched by the slow system. Ks approachesthe small values observed for the isolated case for larger γ.

Since the slow system now covers more of the residual load, the capacities of the moreflexible systems can be reduced. Km is smaller by ≈ 0.1 − 0.15 in the aggregated case,relatively independent of γ. The maximum value is also decreased to 0.3 and shifted to aslightly larger γ = 0.45, indicating that the spatially smoothed VRES generation allowsa higher γ before significant fluctuations and curtailment events occur on the synoptictimescale.

For small γ the Kf in the aggregated system is similar to that of the isolated case, butit increases slower with γ and even reaches a maximum of Kf = 0.65 around γ = 0.9 afterwhich it declines, following the decrease of the total required capacity.

The remaining part of this chapter focuses on the case of an aggregated Europe becauseit allows the largest possible contributions from the slower system, and therefore allows toquantify an upper bound for their required capacities.

26

2.3 Results

0.0 0.5 1.0 1.5 2.0

VRES gross share

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

dispatc

h c

apaci

ties

/ <

L>

AGG DE

TotalDaily

SynopticSeasonal

Figure 2.4: Modelled capacities versus VRES gross share γ. Same as Fig. 2.2, but for aggregatedEurope (solid) in addition to Germany (dotted).

2.3.3 Slow capacities going out of use

The previous section quantified how fast the capacity of the slowly flexible class decreaseswith an increased share of VRES due to its limited ability to follow the volatile behaviourof the residual load. Since the model prefers the use of the slow system whenever possible,these capacities are an upper bound. However, Fig. 2.3 indicated that for VRES grossshares larger than about γ > 50% these capacities cannot often be used to their full extent.This is quantified by the utilization fraction fi defined as the ratio

fi =〈Bi〉Ki

(2.9)

between the mean hourly dispatch 〈Bi〉 and capacity Ki. Fig. 2.5(a) shows fi as a functionof γ. As is typical for baseload systems, the slow system is highly utilized with fi ≈ 80%for small γ. However, with increased γ its average usage rapidly falls off due to morefrequent and longer ramping. Only 50% of its capacity is used on average at γ = 0.5, andless than 10% as soon as γ = 1.

In combination with the decrease of its capacity Kf shown in Fig. 2.4, this results in asubstantial reduction in the amount of average dispatch 〈Bs〉 generated per hour by theslow system. Initially, the contribution of the slow system is large with 〈Bs〉 = 80% of themean load 〈L〉, as shown in Fig. 2.5(b). But already at γ = 50% the slow system has alower average dispatch than the other two systems. Here 〈Bs〉 = 15% which correspondsto just 30% of the total average dispatch. At γ = 100%, 〈Bs〉 is negligible in absolute aswell as in relative terms.

Even though the use of the slow system falls off quickly with the share of renewablegeneration, the medium flexible system is able to compensate for some of the emergingfluctuations in the residual load at intermediate shares of VRES around γ = 50%. Together

27


0.0 0.5 1.0 1.5 2.0

VRES gross share

0.0

0.2

0.4

0.6

0.8

1.0

utilization fraction

(a)


0.0 0.5 1.0 1.5 2.0

VRES gross share

0.0

0.2

0.4

0.6

0.8

1.0

mean dispatch / <

L>h

(b)


Figure 2.5: (a): Utilization fractions fi of the total, fast, medium, and slow systems (magenta,blue, red, green lines), respectively, as a function of the VRES gross share γ for aggregated Europe.(b): Mean hourly dispatch 〈Bi〉t = Kifi in units of the mean load 〈L〉 as a function of γ (samecolor code as in (a)). The dashed black line marks the 1:1 correlation between the increase ofcontributions from the VRES and the corresponding decrease of the total residual demand.

with the increase in medium capacity, its utilization fraction increases slightly in thesescenarios. This leads to a peak in the mean dispatch around γ = 50% where the mediumsystem also contributes roughly one third of the dispatch. For larger γ its utilizationfraction remains highest and is still fm = 25% at γ = 100%, resulting in a mean dispatchof 20% for the total system.

The fast flexibility class is designed to quickly react to the strongest demand fluctuationsthat can not be covered by the slower systems. The utilization fraction of the fast systemis therefore not expected to be very large. Indeed, the utilization ff stays below 40%and declines even further for large γ even though it produces the largest share of backupenergy for γ > 0.5, see Fig. 2.5(b).

The mean dispatch of the total system decreases from 100% proportional to the increas-ing gross share of the VRES until γ ≈ 0.6, indicating that most of the VRES generation isused. For larger γ curtailment begins to play a significant role, such that more installationof VRES leads to less than an equivalent reduction in required backup energy. Most ofthe power at large γ > 1 therefore has to be covered by the fast system.

These results are also reflected in the dispatch duration curves of the backup systemsfor the three cases of γ = 0, 0.5, 1 shown in Fig. 2.6. A dispatch duration curve showsthe fraction of time the dispatch of a given class equals or exceeds a certain value, orequivalently, the hourly dispatch in decreasing order instead of in chronological order.

Fig. 2.6(a) shows the baseload properties of the slow system at γ = 0, as its dispatchnever drops below 62% 〈L〉 and is able to follow the dominant slow seasonal variations.The total dispatch is equivalent to the demand over the time range. The total dispatchduration curve is much less peaked initially than in scenarios with higher VRES shares.At γ = 0.5 only a small fraction of hours is responsible for the highest need for backupgeneration, and therefore for the total capacity.

Fig. 2.6(b) also shows the onset of events with very low or zero residual load, i.e. theoccurrence of a few hours when no dispatchable generation is needed. As indicated before,this is related to the increase of fluctuations of the residual load and can be associated

28

2.4 Model sensitivities

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4dispatch / <L>

γ=0

(a)

20 40 60 80 100

fraction of hours [%]

γ=0.5

(b)

20 40 60 80 100

γ=1

(c)


Figure 2.6: Dispatch duration curves for the three flexibility classes and their sum at γ = 0, 0.5, 1.0(a,b,c), which show the hourly dispatch not in chronological, but in decreasing order againstquantiles of hours. Here 100% of the hours correspond to the 8 years of data.

with the significant decrease in capacity and utilization of the slow system. The modellingchoice to prefer slow dispatch whenever possible leads to different shapes of the dispatchduration curves for the three classes. The slow and medium systems are run at full capacityfor 10% and 20% of the time, respectively, as indicated by the horizontal parts of the linesin Fig. 2.6(b). However, the full capacity of the fast system is required only for a fewextreme events. For about 10% of the time the fast system is not needed even though thetotal demand is almost never zero. This is mostly due to periods with little residual loadwhen the medium system can cover the remaining fluctuations.

For γ = 1, the VRES generation satisfies the demand for about 45% of the time, asshown in Fig. 2.6(c). The residual load is also so volatile that it has to be covered almostentirely by the fast system, with some support from the medium class. The steps in thedispatch duration of the medium system are due to repeated up and down ramping fromzero with the maximum rate while trying to cover short but relatively large peaks in theresidual load that only last a few hours. The height of the steps is therefore a multiple ofthe ramp rate mm × 1h. The slow class is used for only a small fraction of hours in thiscase even though the capacity is already strongly reduced.


2.4.1 Power capacities

The relatively low utilization fractions especially for larger shares of renewables discussedin the previous section 2.3.3 suggest that it might be possible to reduce the optimalcapacities slightly without increasing the amount of the missing energy Emiss dramatically.This was tested by fixing the capacities Ki of two flexibility classes to their optimal valuesfor a given γ while reducing the capacity of the third class in small steps of 0.025 〈L〉. Afteroptimizing the dispatch of the three systems according to the objective function (2.2) again,but with these fixed Ki, the resulting Emiss =

∑t(LR −

∑iBi)+ can be calculated.

The results are shown in Fig. 2.7(a) for capacities that result in Emiss = 20 to 70 av.l.h.in eight years, i.e. starting from the initial 99.97% covered energy and decreasing one

29


0.20.40.60.81.0

Kf/<L>

0.20.40.60.81.0

Km/<L>

0.0 0.5 1.0 1.5 2.0

VRES gross share

0.00.20.40.60.81.0

Ks/<L>

20

30

40

50

60

70

Emiss[av.l.h.]

(a)

0.20.40.60.81.0

Kf/<L>

0.20.40.60.81.0

Km/<L> 2.0 20.0 70.0

0.0 0.5 1.0 1.5 2.0

VRES gross share

0.00.20.40.60.81.0

Ks/<L>

(b)

Figure 2.7: (a): Sensitivity of missing energy Emiss to the reduction of one of the fast, medium,slow (top to bottom) capacities while the other two are fixed at their optimum value, as a functionof γ for aggregated Europe. Color-coded is Emiss in units of av.l.h. in eight years. In the whiteareas above/below, Emiss is lower/higher than the color range. (b): Sensitivity of the capacities ofthe fast, medium, slow systems (top to bottom) on the allowed missing energy for Emiss = 2, 20, 70av.l.h. over eight years (black, red, cyan lines) as function of γ for aggregated Europe.

capacity only until 99.9% of the energy is covered. The latter corresponds to full coverageof the demand for roughly 97% of all hours at γ = 0.3. In the top panel, only the capacityKf of the fast component gets reduced, but this quickly results in a total Emiss > 70av.l.h., especially at small γ. Since the fast systems are dispatched last and their capacitylargely determines the amount of Emiss, this shows that the optimized solution is robust,because small deviations from the optimum Kf lead to a large change in Emiss and in theobjective function.

The capacity of the medium system (middle panel) can be lowered slightly more, fromKm = 0.275 〈L〉 to 0.175 〈L〉 at γ = 0.5, without increasing Emiss above 70 av.l.h. becausethe fast systems can compensate occasionally by increasing their utilization fraction. Thisalso shows that the capacities for the slower flexible systems is an upper bound, and thethird term in the optimization function is important to control the dispatch order.

If varying the slow capacity (bottom panel), Emiss > 70 av.l.h. is only reached once Ks

is smaller than its optimum value by up to 0.2 〈L〉 at γ ≈ 0.5 − 0.7, e.g. by decreasingKs from 0.2 〈L〉 to 0.05 〈L〉 at γ = 0.6. This also means that Ks can be set to zero forγ > 0.7, i.e. decommissioning of all slow capacities, without reducing the total amount ofcovered energy below 99.9%, if the other two systems are at their optimum capacities. Themedium capacity (middle panel) can only be reduced to zero in this way while Emiss < 70av.l.h. for large γ > 0.9.

2.4.2 Missing energy

In Fig. 2.7(b) the previous analysis is reversed: Emiss is fixed via Eq. (2.3) and the mixof backup capacities is optimized for different γ. Mainly the capacity of the fast systemshown in the top panel reacts to an increased tolerance for Emiss. Kf decreases from 80%to 50% 〈L〉 at γ = 1 between Emiss = 2 and 70 av.l.h. in eight years. The capacities of the

30


0.0 0.5 1.0 1.5 2.0

VRES gross share

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

dispatch capacities / <L> mi factor

0.512

Figure 2.8: Modelled capacities assuming half (dotted) and twice (dashed) the reference (solid)ramp rates (mf remain unconstrained), respectively, versus γ for aggregated Europe. Total, fast,medium, slow capacities are shown as magenta, blue, red, green lines. Solid lines are the same asin Fig. 2.4.

less flexible systems change much less, only Km decreases slightly by less than 0.07 〈L〉 forγ < 1. This supports the previous finding that the largest capacities are mostly requiredto cover a few events on a short timescale.

2.4.3 Ramp rates

Another important aspect of the model are the ramp rates that were chosen to match thetypical timescales of variations in the renewable generation and consumption, see Sec. 2.2.In order to assess the sensitivity of the results to these parameters, Fig. 2.8 comparesthe modelled capacities assuming half and twice the ramp rates, respectively. Only theflexibilities of the medium and slow systems were changed, and the fast system is stillassumed to be unconstrained.

The total capacities are virtually unchanged in all cases as only the relative mix betweenthe capacities changes. If larger ramp rates are assumed, the slow system can contributemore and Ks increases by 0.04 − 0.06 〈L〉 for γ < 1. The largest differences are aroundγ = 0.5−0.7 where the benefits are greatest for a more flexible slow system that is able toramp up and down between the increasing number of events with zero residual load. Thereversed argument holds for the case with only half the reference ramp rates, leading toslightly decreased Ks for all γ. The differences in Km are very small, especially around itspeak at γ = 0.5. This suggests that most of the benefits of increased ramp rates can beused by the slow class, except at very small and large γ. As the capacity of the fast classis mostly influenced by the need to reduce missing energy, Kf adapts to the changes ofthe other capacities accordingly, and is higher and lower relatively independent of γ if theother systems are less and more flexible, respectively. Overall, the capacities are relativelyinsensitive to the choice of the ramp rates as higher flexibilities lead to a slight shift fromfast to slow capacities, but the qualitative results remain unchanged.

31


Missing and excess energy of the optimized system are not influenced by variations ofthe maximum ramp rate, as they only depend on the capacity weights in accordance withequations 2.3 and 2.8 in section 2.2.2.

2.5 Discussion

Some aspects of the simplified model deserve some attention. First, there is the issueof the missing energy that is allowed for. The current electricity supply is designed formuch higher security of supply than assumed in this chapter. However, the treatmenthere can be justified by considering a backup system as only one part of an electricitysupply complementing VRES. It is likely that future energy systems become more flexible,including new mechanisms like storage and demand-side management, simply because itis more economical to use these other options than to cover each and every demand as ifit were a static boundary condition [55]. In such an environment, it is likely that therewill be means to control those extreme hours not yet covered by the dispatchable backupsystem.

Furthermore, the ramp rates in this study are well below the technical limits of typicalpower plants [53]. They are chosen to effectively model the whole inertia in plant dis-patch, which is not only due to technical constraints, but also to regulatory and economicconditions. Therefore, a slow capacity of zero does not necessarily mean that all slowlyflexible power plants have to be shut down. Rather, these plants can still operate, but withshorter notification times, more cycling, and fewer full load hours, such that they wouldfall into the medium flexibility class in the terminology of this chapter. This upgrade ofalready existing slow plants could also be an economically viable way to at least partlycover the γ ≈ 0.3 − 0.5 peak of medium flexible capacity. Detailed economic feasibilitystudies of flexibility upgrades e.g. via enabling fuel switching in power plants support thisassumption [56]. However, a clear trend towards more flexible power plants remains.

Sub-hourly fluctuations in consumption and VRES generation are not covered in themodel. However, the wind generation power spectrum suggests that hourly/multi-hourfluctuations are dominant (i.e. stronger than sub-hour) [57] and therefore additional ca-pacity needs to cover high-frequency fluctuations can be expected to be small, especiallyif aggregation benefits at least at a regional level can be assumed [58].

2.6 Comparison to the current German system

The optimal slowly flexible capacity decreases strongly from the dominant system com-ponent to almost zero contribution with increasing share of renewable generation. Thissuggests a large shift of the current power plant portfolio away from slow flexibility. Atimescale for this modelled shift can be approximated by mapping values of the renewablegross share γ to years in the future, even though the model was not designed to optimizea pathway solution. This mapping is based on a logistic fit to historic and targeted windand solar PV penetrations in Germany for the years 1990 to 2050, as described by [49].These authors use the 2020 targets defined in Germany’s National Renewable Energy Ac-tion Plan [29], and assume γ = 100% for 2050. The optimized capacities as a function oftime are shown in Fig. 2.9.

32

2.6 Comparison to the current German system

2000 2010 2020 2030 2040 2050

year

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Capacity / <L>

Daily Synoptic Seasonal

lifetime30 yrs35 yrs40 yrs

0.1 0.3 0.5 0.7 0.9VRES gross share

Figure 2.9: Comparison between the modelled and estimated remaining slowly flexible capacitiesin isolated Germany as function of time. The modelled slow, medium, and fast (green, red, bluelines) capacities are the same as in Fig. 2.2 but with the VRES gross share transformed to yearsas described in the text. The black lines show the expected decommissioning of currently installedslowly flexible nuclear, lignite, and coal power plants in Germany if lifetimes of either 30, 35,or 40 years (dotted, solid, dashed lines) are assumed. Their current (2014) capacity withoutdecommissioning is marked by the black diamond.

In order to assess the impact of this shift in the currently installed generator fleet, theexpected remaining lifetime of the slowly flexible capacity in Germany is estimated asdescribed in the following. From the complete list of German power plants provided by[59], all nuclear, lignite and coal power plants that are older than 10 years, i.e. builtbefore 2004, are included. More recently installed or renovated plants are assumed to bealready capable of a more flexible efficient operation. If these slowly flexible power plantswould be decommissioned after a fixed economic lifetime of n = 30, 35, or 40 years, theremaining installed capacity as function of time is also shown in Fig. 2.9. Some of thegenerators already operate longer than 40 years without major renovation and would bedecommissioned immediately in this scenario.

Under these assumptions, the decrease of the optimized slow capacity in Germany hap-pens on a similar timescale as the end of economic lifetime decommissioning of installedcapacity, especially for an assumed lifetime of 35 years. This implies that in this scenariowhere electricity production is the only source of flexibility, no additional slowly flexiblegenerators should be built. It also suggests that most of these generators can be utilizeduntil the end of their economic lifetime, if favourable conditions are assumed, and do nothave to be decommissioned ahead of time.

33


2.7 Conclusions and Outlook

A simplified capacity and dispatch optimization model of the European power systemwas used to determine the amount of VRES gross share γ above which power plants canno longer be run in baseload mode. An important contrast to bottom-up models withindividual plants is that this model is independent of the details of the dispatchable powerplant fleet, such as the plant number–size distribution or the detailed ramp potentialsof individual power plants in different states. As seen in Sec. 2.4 and 2.8, the results arestable under changes in the physico-technical assumptions as well as the weight parametersof the model.

For isolated countries, the phase-out of slowly flexible capacities comes at about γ ≈50%, for aggregated Europe, at about γ = 50%− 70%. From then on, power plants thattoday are used for baseload requirements will have to be run in a higher flexibility class – orbe decommissioned if this is not economically and/or ecologically feasible. This increasesthe demand for plants that are more efficient and more economical when cycled regularly.

The need for medium flexible plants first rises in parallel with the decrease in needfor baseload plants, until it peaks at γ = 35% and γ = 45% for isolated countries andaggregated Europe, respectively. This is due to the growing fluctuations in the residualload on the synoptic timescale that can be followed by the medium flexible class. Forhigher γ, the typical fluctuation timescales become too short for the medium system, sothat it can support the fast system decreasingly well until it contributes only 20% of theenergy at γ = 100%.

In contrast, the highly flexible capacity is seen to rise sharply, once the fluctuations ofthe residual load become too large for the slower systems. The capacity goes up from 30%of the average load to 50% and 60% at γ = 50% and further up to 65% and 85% at largeγ = 100%, for the aggregated and isolated cases, respectively. At that point it is used tocover almost the entire residual load in both cases.

If countries are regarded as isolated entities, the total power capacity of the dispatchablesystem is seen to decrease by only 19%, even at an extreme VRES gross share of γ =200%. Here, Europe-wide sharing of dispatchable resources could significantly reduce therequirements by about 60% at γ = 200%.

Nonetheless, the large and rarely needed capacities still pose severe problems. In or-der to reduce these capacities further, a future energy system should be considered thatincludes storage and demand-side-management within the electricity sector, as well ascouplings to other energy sectors, similar to those proposed in e.g. Ref. [41], where theelectricity sector is coupled to heating/cooling via heat pumps and power-to-gas, and tothe transport sector by electric vehicles and electrically generated synfuels (see also [42]).This is also expected to increase the relative share of slowly flexible systems due to con-siderably reduced fluctuations in the residual load. These couplings will be investigatedin a future extension of the model. Beyond that, limited transmission will be included tointerpolate between the two extreme cases of isolated countries and an aggregated con-tinent. Furthermore, the uncertainties associated with limited prediction horizons andforecast errors will also be included. All of these considerations will help to develop a newand efficient planning tool for emerging large-scale renewable electricity systems.

34

2.8 Appendix: Modelling details

0.0 0.5 1.0 1.5 2.0

VRES gross share

92

93

94

95

96

97

98

99

100

Quantile of covered hours [%]

Emiss [av.l.h]2.020.070.0

AggDE

Figure 2.10: Quantiles of the number of covered hours at Emiss = 2, 20, 70 av.l.h. in eight years(black, red, cyan) as a function of VRES gross share γ for aggregated Europe (solid) and isolatedGermany (dotted).

2.8 Appendix: Modelling details

2.8.1 Unserved hours

One important aspect of the modelling approach is to allow for a small amount of mismatchbetween residual load and the backup dispatch. The relation Emiss =

cwfast

2 in Eq. (2.3)gives a good handle for the control of the unserved energy. The reference value of Emiss waschosen to guarantee security of supply, i.e. exact residual load matching, for approximately99% of all hours. For that, an hour is defined to be unserved if the total dispatch is smallerthan the demand by LR(t)−

∑iBi ≤ 10−4 〈L〉 in order to avoid numerical artefacts. The

quantile q = 1−NmissT of fully covered hours is then calculated from the number of partially

unserved hours Nmiss over the full time range T of the data.

Fig. 2.10 shows q as a function of γ for given Emiss. It indicates that for small sharesof renewables there are few extreme outliers in the demand and the allowed amount ofmismatch can be distributed over many hours. However, with increasing γ there is aconcentration of the missing energy to fewer, more extreme hours. For higher Emiss thenumber of unserved hours also increases. At the reference value Emiss = 20 av.l.h. securityof supply is given for at least a quantile of q > 99% for all γ > 30%.

The effect of aggregation is not very large in this case. The allowed Emiss is distributedover slightly more hours around γ = 0.5 in the aggregated case, indicating a smootherresidual load. But at larger γ the most extreme events occur also on a large spatial scaleand are not easily mitigated just by transmission.

2.8.2 Sensitivity to capacity weights

The relative weights wi of the capacities Ki where chosen such that the fast class has thelargest weight, i.e. Kf is as small as possible. If the ratio between the wi is not set to

35


0.0 0.5 1.0 1.5 2.0

VRES gross share

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

dispatch capacities / <L> wi

4:2:1100:10:1

Figure 2.11: Modelled capacities assuming relative ratios of the capacity weights wf : wm : ws =4 : 2 : 1 (solid, reference model) and 100 : 10 : 1 (dashed) versus γ for aggregated Europe. Total,fast, medium, slow capacities are shown as magenta, blue, red, green lines. Solid lines are the sameas in Fig. 2.4.

wf : wm : ws = 4 : 2 : 1 as in the reference model, but to 100 : 10 : 1, i.e. the weightof the fast class is even more dominant, the quantitative results change slightly, but thequalitative behaviour is the same, as shown in Fig. 2.11. The major difference is thatthe fast capacity is decreased only slightly by less than 0.03 〈L〉. But since the amount ofallowed uncovered energy Emiss is still the same, the medium and slow capacities have tobe increased over-proportionally by up to 0.1 〈L〉 and 0.09 〈L〉, respectively, to provide thesame security of supply for a few more extreme hours. The total capacity therefore is alsolarger by up to 0.15 〈L〉. Not shown, the amount of overproduced energy increases andthe utilization fraction decreases as the less flexible systems are less efficient in reachingthe peaks of the residual load that were covered before by the additional capacity of thevery flexible fast system.

2.8.3 Sensitivity to dispatch weights

The model optimization shows that the relative weights vi in the utilization term in theobjective function (2.2) do not influence the quantitative results, as the differences betweenthe reference ratios vf : vm : vs = 4 : 2 : 1, and 100 : 10 : 1 are negligible. This is expectedbecause this term was mainly intended to lift the degeneracy in the dispatch order for agiven capacity mix, and therefore has a small weight d. In this case a reversed order of theweights would not change the optimal capacities, but dramatically reduce the utilizationfraction of the medium and slow components in favour of the fast system.

36

3 Backup Flexibility and Storage

3.1 Introduction

In the previous chapter the dependence of the flexibility requirements of an energy networkon the fraction of renewable energy sources were studied, using a rather simplified modelcontaining only three classes of dispatchable generators neither including an energy storagesystem nor allowing a restricted transmission network expansion. In this chapter theinclusion of an energy storage system will be studied in detail. Storage systems can be animportant source of flexibility even though they are not net generators. However, they canshift overproduction from other sources to later points in time when the demand is highand thereby reduce curtailment, improve the usage of renewable generators, and reducesome of the volatility so that cheaper, slower generators can be better exploited. Theadditional effects of a restricted transmission network expansion will be addressed in thesubsequent chapter 4.

The energy storage system is introduced as an additional option for flexibility that can beexpanded according to its techno-economic efficiency. In order to allow a fair comparisonof the economic benefits, this also requires to explicitly consider current conventional gen-erator technologies with realistic economic cost assumptions. The model used to achievethese goals is described in section 3.2, and the impact of these changes will be presentedin section 3.3.

3.2 Methods

As in the previous chapter, the model still tries to cover the residual load, after all avail-able renewable generation was used, by optimizing the capacity and dispatch of threeclasses of conventional dispatchable generators with different flexibilities defined by theirmaximum ramp rates. However, in contrast to the previous model where abstract classesof generators were considered, in this model the three flexibility classes are representedby five concrete conventional technologies with economic cost assumptions. The storagetechnologies are included as new sets of optimization variables that describe charge anddischarge operation and capacity as well as the resulting state of charge, and also havecosts associated with their installed capacities. This allows to formulate the model asa linear techno-economic optimization that minimizes the total system costs. The totalsystem cost is composed of annualized capital investment costs cs of the capacity Ks ofgenerator and storage technologies s, and the operation costs os,t for their dispatch Bs,tin hour t. The optimization problem is then

minKs,Bs,t

(∑s

csKs +∑s,t

os,tBs,t

)(3.1)

subject to the following constraints:

37


• The energy in the system has to be conserved in each hour by matching generationand demand: (

Lt −GRt)+

=: LR,t =∑s

Bs,t − Ct +Dt ∀t (3.2)

The amount of hourly demand Lt that can not be covered by renewable generationGRt is called the residual load LR,t. In order to ensure security of supply in thesystem, a combination of backup generator or storage dispatch Bs,t has to cover theremaining amount of power. It might be cost efficient to over-produce electricity insome hours due to ramping constraints of the slower generators which then has tobe curtailed (Ct ≥ 0). Additionally, a limited amount Dt of the load can be shed ifthe system is not flexible enough.

• The dispatch of generators and storage can not exceed the installed power capacityby definition:

0 ≤ Bs,t ≤ Ks ∀t (3.3)

• The maximum ramp rates mi of the three conventional generator classes i = definedin the previous chapter are also enforced here:∣∣∣∣dBs,tdt

∣∣∣∣ ≤ mi (3.4)

For that purpose the five conventional generator technologies considered here aredivided into the three backup flexibility classes as listed in Tab. 3.1. In order toallow a better comparison with the previous results, the capacities and dispatchedenergy of the technologies in each class are later summed up for the analysis of theresults.

• Charging and discharging the storage units determines their state-of-charge socs,t:

socs,t = socs,t−1 + ηsBs,t,charge − η−1s Bs,t,discharge (3.5)

0 ≤ socs,t ≤ Ks,t,energy ∀s, t (3.6)

All storage operations cause a fraction η of energy losses such that the round tripefficiency is η2. The soc can not exceed the installed energy capacity Ks,t,energy.It is also required to be equal in the first and the last hour T of the simulationsocs,t=0 = socs,t=T to allow optimal storage use also at the start of the modelledtime period.

• In order to approximate the security-of-supply requirements assumed in the previouschapter, the amount of load sheddingDt is strongly limited in both power and energy:

Dt ≤ Dmax = 0.25 〈L〉 ∀t (3.7)

〈Dt〉 ≤ Dtot,max = 0.01% ·Dmax (3.8)

A maximum of one quarter of the mean load can be shed per hour, but only in upto 0.01% of the hours, slightly less than one hour per year, such that 99.9975% ofthe energy demand has to be covered. This is a very strict limit to the security ofsupply, but helps to avoid a few extreme events in the residual load time series.

38

3.2Meth

ods

Table 3.1: Input parameters based on 2010 value estimates from [60] unless stated otherwise.

Technology flexibility max. capital fixed variable life- efficiency fuel CO2

classa ramp cost O&M cost time costb intensityratea [AC/kW] cost [AC/MWh] [a] [AC/ [t/kWht][%〈L〉/h] [AC/kW/a] MWht]

OCGT fast ∞ 400 15 3 30 0.3 21.6 0.27CCGT medium 2.26 800 20 4 30 0.6 21.6 0.27hard coal medium 2.26 1300 25 6 40 0.46 8.4 0.32lignite slow 0.25 2000 30 7 40 0.39 2.9 0.45nuclear slow 0.25 4000 0 8 50 0.33 3 0.27

Technology capital fixed variable life- efficiency capitalcost O&M cost time cost per[AC/kW] cost [AC/MWh] [a] energy

[AC/kW/a] storage[AC/kWh]

hydrogenc 1268 20.7 0 20 0.438 21.2central 529 9.3 0 20 0.9 240batteries(LiTi)c

a From previous chapter.b Does not include the CO2 emission price of 20 AC/t.c Budischak et al. [61].

39


The three abstract flexibility classes are modelled as five conventional technologies byassuming respective maximum ramp rates of the power output as defined in the previouschapter. The five technologies are open cycle gas turbines (OCGT) as fast flexibility,combined cycle gas turbines (CCGT) and hard coal as medium flexibility, and lignite andnuclear power plants as slow flexibility class.

It is important to consider realistic cost assumptions to allow the inclusion of expandablestorage technologies in the model, for which relative weights can not be readily defined.Storage can provide flexibility to the system by temporally delaying the consumption ofenergy that was generated earlier, minus losses. Therefore, it links consecutive snapshotsof the model and requires simultaneous optimization over an extended period. The effectsof adding two types of storage technologies are tested here. Stationary batteries represent ashort-term storage, while longer term storage is modelled as H2 storage that can be chargedby electrolysis and discharged via fuel cells, following the assumptions of [61]. Theircapacities can be optimized in the model without restrictions other than their economicalcosts.

Furthermore, a more recent time window from 2010 to 2014 with more accurate inputdata of weather-based generation and electricity consumption is used here, instead of theperiod 2000 to 2008. The conversion of weather data to potential renewable generationtime series remains as described in the previous model.

3.3 Results

3.3.1 Comparison with the previous model

The model presented here uses a similar concept as the model in the previous chapter butmakes a few significantly different assumptions, and therefore it is important to quantifythe introduced changes. The total amount of installed backup capacity is shown in Fig. 3.1.It is very comparable to the results obtained with the previous model, but is slightlylarger by 3% to 7%. Also the qualitative behaviour of the capacities of the three classesare similar in both models despite some quantitative differences. The slow capacity nowdecreases linearly with increasing share of renewables. It reaches zero once it can no longercontribute significant amounts of energy to the system instead of retaining a finite capacitywith very low utilization. This is due to the reversed order of the capacity weights thatenforces economic efficiency. In the previous model, the slowly flexible class had the lowestpower capacity weight in order to determine its upper bound, while here it has the highestassumed cost.

The intermittent need for medium flexible capacity is similar in both models with apeak in capacity for renewable shares close to 50% followed by a slow exponential decaywith increasing renewable penetration. However, the quantitative differences are largestin this flexibility class as the capacity is now systematically larger and the capacity peakis shifted towards higher renewable shares of 60% to 80% instead of 40%. This shift islarger, but the absolute difference of the capacities between the models become smallerif interconnecting transmission is allowed and can be used to smooth out some of thefluctuations of the residual load.

The fast flexible capacity shows a similar trend as in the previous model of increasingfrom a relatively small share to the dominant class of backup generator technology inhighly renewable systems. However, it now increases with a more constant slope with

40

3.3 Results


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6Ki

DEno storold Objtotalfastmediumslow


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Ki

AGGno storold Objtotalfastmediumslow

Figure 3.1: Left: Optimal backup capacities in units of the mean load versus VRES gross shareγ for the model presented here but still without storage (solid lines, “no stor”) and the modelin the previous chapter 2 (dashed lines, “old Obj”) for Germany. Right: Same for aggregatedEurope. The blue, red, and green lines correspond to the fast, medium, and slow flexibility classes,respectively. The sum of the three capacities is given by the magenta line.

increasing renewable share as the larger installations of medium capacity, and especiallyits higher peak, can help to cover more demand peaks. In the case of aggregated Europe,unlike in the previous model, the fast capacity grows monotonically and has no peak forrenewable gross shares of up to 2. However, it can be expected to decrease for even largerpenetrations as it is the only remaining technology with sufficient flexibility at this point.The partial substitution of fast capacity by a larger medium capacity suggests that therelatively cheaper energy from the medium flexible generators compared to the fast flexibleclass, with a cost ratio of ofast : omedium = 2.13 : 1 instead of 2 : 1, has a larger impactthan the reversal of their relative capital cost ratio to 1 : 2.19 from 2 : 1 in the previousmodel.

3.3.2 Addition of storage technologies

The use of explicit cost assumptions allows to integrate storage technologies with appropri-ate economic weights into the model and to analyse their impact on flexibility requirementsin the system. The influence of the two storage technologies batteries and hydrogen (H2)storage on the modelled backup capacities is shown in Fig. 3.2. In both considered trans-mission scenarios, the installed storage power capacity is almost zero if no renewablesare in the system and increases slowly with the penetration of renewable generation to amaximum close to 10% of the mean load at values of γ slightly larger than where the peakof the medium flexible capacity is located. It then returns to zero for very large renewablepenetrations of γ = 1.3 to 1.5. The battery storage systems have a larger optimal powercapacity and a larger effect on the backup power capacities than H2 storage, as discussedbelow. The total backup capacity is reduced by almost exactly the amount of installedstorage power capacity, which indicates that the total backup capacity is still determinedby the most extreme demand peak.

For both storage options, the reduction of fast flexible capacity is proportional to theinstalled storage power with a proportionality factor of around 1.2, i.e., the fast capacitycan be reduced by more than the installed storage power. At the same time, the medium

41



0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

dispatch capacities / <L

>

DEno storH2batterytotalfastmediumslow


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

dispatch cap

acities / <L

>

AGGno storH2batterytotalfastmediumslow

Figure 3.2: Left: Modelled optimal backup capacities in units of the mean load versus VRESgross share γ for Germany if either of the storage options no storage, battery, or H2 storage (solid,dotted, dashed lines) is included. The power capacity of battery and H2 storage are marked asdotted and dashed black lines, respectively. Right: Same for aggregated Europe. Same color codeas in Fig. 3.1.

flexible capacity is increased, albeit by a smaller factor. The increase of medium flexiblecapacity is equivalent to 70% of the installed battery power and around 40% of the H2

storage power, respectively. The slowly flexible capacity is reduced only slightly by bothtypes of storage, but batteries also have a larger effect here.

Despite the differences in both absolute and relative changes of the backup power ca-pacities, their mean energy dispatch is virtually identical between the two storage options,as plotted in Fig. 3.3. For both storage technologies, the same small amount of energygeneration is shifted from fast to medium flexible generators without a net change of totaldispatch. Only the use of batteries allows to also reduce the mean dispatch of slowlyflexible generators. This leads to a decrease of the total backup energy of up to 3% of themean load compared to the scenario without storage.

The very similar amounts of generated energy in the two storage scenarios despite thelarger changes in backup power capacity caused by the inclusion of batteries shows that thetwo storage technologies act on different timescales. This is supported by their differenttechno-economic parameters. Batteries have low assumed costs for power capacity buthigh costs for energy capacity and a very high round trip efficiency, which makes themsuitable for short-term, high through-put storage. Therefore, they can smooth some of thehigh frequency fluctuations of the renewable generators. This reduces the need for fastcapacity and makes a larger amount of medium capacity economically efficient withoutchanging the net energy generation strongly. If more than half of the energy is generatedby renewables, the batteries can reduce the total backup energy slightly due to betterutilization of curtailed energy especially from solar PV.

In contrast, H2 storage has high power- but low energy storage capacity costs and arelatively low round trip efficiency, supporting a longer term storage of larger amounts ofenergy. This leads to a relatively large increase in dispatch of medium flexible generatorsdespite the small addition of capacity. The lack of change in the use of slowly flexiblegenerators indicates that an expansion of the H2 storage capacity to a size that is relevantfor seasonal balancing is not economically efficient. The storage systems have no assumed

42

3.3 Results


0.0

0.2

0.4

0.6

0.8

1.0

1.2mean dispatch / <L

>hDE

no storH2batterytotalfastmediumslow


0.0

0.2

0.4

0.6

0.8

1.0

1.2

mea

n dispatch / <L

>h

AGGno storH2batterytotalfastmediumslow

Figure 3.3: Left: Average dispatched backup energy versus VRES gross share γ for Germanyif either of the storage options no storage, battery, or H2 storage (solid, dotted, dashed lines) isincluded. Right: Same for aggregated Europe. Same color code as in Fig. 3.1.

ramp rate constraints, allowing H2 storage to use e.g. otherwise curtailed renewable energyto be used for highly flexible short-term balancing despite the relatively low round tripefficiency.

In the single node scenario of an isolated Germany, spatial smoothing via transmission isrelatively ineffective and therefore the residual load starts to fluctuate strongly with shortbut high peaks once more than half of the electric energy is generated by renewables, asshown in the previous chapter. These spikes require a large power capacity but representonly a small amount of energy, as indicated by the continuously high need for backupcapacity even though the dispatched energy decreases strongly. Since the power capacityof the highly flexible gas turbines is assumed to be less expensive than the storage powercapacity of batteries (and H2 storage), it is more cost-efficient to cover these high, shortpeaks with a small amount of natural gas consumption than to build storage systems thatcannot be utilized most of the time. Therefore, no storage is built at very high shares ofrenewable generation when the total residual load is small and concentrated to a smallnumber of hours.

Unlimited transmission in Europe smoothes many of these extreme peaks in the residualload. This leads to a lower required peak capacity and increases the ratio of dispatchedenergy against power capacity that the backup system (including storage) has to provide.Therefore, the installed storage capacity continues to increase up to a renewable share ofaround 80%. At this share, the installed storage capacity in the case of aggregated Europeis larger than for isolated Germany because the cost-efficiency of storage relative to theuse of gas turbines can be improved by the spatial smoothing.

The influence of storage on the total cost of the backup system is relatively small.The optimized use of batteries can reduce the costs by up to 2.5%, while H2 storage candecrease it by only up to 1%. However, this model can not quantify the cost benefits thatarise due to the use of curtailed renewable energy that might allow a reduction of theamount of installed renewable generators.

43

4 Backup Flexibility, Storage,Hydroelectricity and InternationalTransmission1

4.1 Introduction

The European Council has set the goal to reduce CO2 emissions in the European Unionby between 80% and 95% in 2050 compared to their 1990 values [63]. Most Europeancountries will rely on renewable energy sources to reach this goal. Although the majorityof renewable energy comes from hydroelectricity today, the renewable sources with thegreatest expansion potential are wind and solar energy.

The strong weather-dependent variations of wind and solar generation present a chal-lenge to the balancing of production and demand in the electricity system. These variationshave particular spatial scales (wind speeds have a correlation length of several hundredsof kilometres) and temporal scales (both solar and wind have daily variations, but alsoseasonal patterns and synoptic-scale variations of multiple days as large weather systemspass). The countries of Europe are small enough that the wind and solar generation insideeach country is highly correlated. This means that if each country has to balance its ownelectricity generation, it must be able to deal with the extreme highs and lows of windand solar generation by itself. Because exploitable hydroelectricity sites are limited andgeographically very unevenly distributed, and backup generation from fossil fuel plants isrestricted by the CO2 cap, the rest of the balancing must come from storage solutions or,in part, from demand side flexibility. The need to invest in storage, on top of generationassets, tends to make these electricity systems expensive [64, 65, 66].

The alternative is to balance the fluctuations of wind and solar in space with inter-connecting transmission between countries, rather than in time with storage. These solu-tions require networks on the continental scale in order to smooth over the varying feed-incaused by synoptic-scale weather systems. Since the costs of the required transmissioninfrastructure are significantly lower than either storage or generation assets, these sys-tems tend to be more cost-effective than storage-based systems [64, 65, 43, 67, 68, 69, 70].However, they require large expansions of transmission capacity that seem implausible inthe face of low public acceptance for overhead power lines [71].

Previous studies have explored the extreme points of this dichotomy between networksand storage [64, 65]. The main innovation of this work is to interpolate smoothly between acontinent-scale network-dominated system and a locally-balanced storage-dominated sys-tem by continuously varying the allowed volume of transmission inter-connectors, fromzero up to unlimited interconnection. This reveals non-linearities in the behaviour ofsystem costs as transmission is expanded. It is shown that most of the benefits of grid

1This chapter has been published as Schlachtberger et al. (2017) [62] and was only slightly modified forthis work.

45

4 Backup Flexibility, Storage, Hydroelectricity and International Transmission

expansion can be achieved with only a moderate expansion, which is an important conclu-sions for policy-makers confronting public acceptance issues arising from new transmissionprojects.

This study falls into a class of studies of the future European electricity system whereload and generation are aggregated at the country level. It follows the work of [64, 65] bytaking a cost-optimal linear programming approach to investment while restricting CO2

emissions, but unlike these studies it explores parameter sweeps in the space of solutions toreveal non-linear effects as constraints are continuously tightened. The parameter spaceapproach can also be found in the more stylised studies of [28, 49, 68, 72], where theeffects of different shares of wind and solar energy on backup generation and transmissionneeds are explored. In contrast to those parametric studies, the results here incorporaterealistic modelling of hydroelectric resources, given their importance as an existing sourceof low-carbon backup flexibility, other sources of storage, a fully heterogeneous allocationof wind and solar capacities to countries within geographic potentials, and a focus on CO2

reduction rather than increasing available renewable energy. The study [73] introduces acost-optimal, heterogeneous allocation of wind and solar capacities around Europe, findinga sizeable reduction in total costs compared to homogeneous distributions, but does notincorporate hydro, storage or CO2 reduction in the modelling. A genetic algorithm is usedin [74] to optimise capacities and dispatch over three years in Europe, the Middle Eastand North Africa to compute storage requirements, but does not incorporate reservoir orrun-of-river hydroelectricity.

Other classes of studies of the optimal European electricity system model the transmis-sion networks of each country in more spatial detail [75, 69], but because of computationallimits, they can only consider a small number of representative weather conditions, whichcannot capture the full spatio-temporal correlations across the continent. In contrast, thisstudy considers a full year of weather situations. Other studies only optimise the transmis-sion expansion while fixing the generation fleet [75, 43, 67, 70]; this has the disadvantagethat the optimisation cannot weigh up whether it is better to build renewables far fromload centres and transport the energy, or build renewables closer to demand. In this studygeneration and transmission capacities are optimised jointly.

The study presented here only considers the electricity sector. Coupling electricity to thetransport, heating, cooling and industrial energy sectors may provide additional sourcesof flexibility that can help to integrate variable renewables. Studies of sector couplinghave in the past either considered single countries (see e.g. Denmark [41, 76], Germany[77, 78, 79], and Ireland [80]) or considered the whole of Europe but without optimisinginternational cooperation [81]. In an upcoming paper we will consider a full optimisationof electricity, heating and transport in the European context. Preliminary results [82] showthat the coordinated charging of battery electric vehicles and thermal energy storage canreplace much of the need for stationary electricity storage when transmission expansion isrestricted.

A further distinction of the model presented here is that the modelling framework usesfree software [83] and all the model-specific code, input data and output data will beavailable online [84], in order to further the transparency and reproducibility of the results.

In this chapter first results from our study are analysed, starting with an introduction tothe mathematical model in Section 4.2 and the data inputs in Section 4.3. In Section 4.4the results are presented from the point of view of total costs, energy production and theinterplay between spatial distribution and temporal variations. Finally in Section 4.5 the

46

4.2 Methods: Model

results are discussed and compared to other studies in the literature, before conclusionsare drawn in Section 4.6.

4.2 Methods: Model

In this study a future, highly renewable European electricity network is modelled. Thecapacities and dispatch of renewable energy generators are optimised within each countryaccording to their geographical and weather-dependent potentials, with the goal of reach-ing ambitious CO2 reduction targets. Examples of the output capacities can be found inFigure 4.4, while a sample dispatch for a single country is shown in Figure 4.9.

4.2.1 Objective function

The model is formulated as a techno-economic linear optimization problem that mini-mizes the total annual system costs. If nodes are labelled by n, generation and storagetechnologies at the node by s, hours of the year by t and inter-connectors by `, then thetotal annual system cost consists of fixed annualised costs cn,s for generation and storagecapacity Gn,s, fixed annualised costs c` for transmission capacity F` and variable costs on,sfor generation and storage dispatch gn,s,t. Costs are not associated with the flow f`,t oninter-connector ` in hour t. The objective function is then

minGn,s,F`,gn,s,t,f`,t

(∑n,s

cn,sGn,s +∑`

c`F` +∑n,s,t

on,sgn,s,t

)(4.1)

The optimization has to satisfy a number of constraints described in the following.

4.2.2 Power balance constraints

To ensure a stable operation of the network, energy demand and generation have to matchin every hour in each node. If the inelastic demand at node n and time t is given by dn,tthen ∑

s

gn,s,t − dn,t =∑`

Kn`f`,t ↔ λn,t ∀n, t (4.2)

where Kn` is the incidence matrix of the network.The Karush-Kuhn-Tucker (KKT) multiplier λn,t associated with the constraint indicates

the marginal price of supplying additional demand at node n in hour t, also known as theLocational Marginal Price (LMP). The value of λn,t at the optimal point is an output ofthe optimisation. Background on the use of KKT duality in electricity markets can befound in [85, 86].

4.2.3 Generator constraints

The dispatch of conventional generators is constrained by the capacity Gn,s

0 ≤ gn,s,t ≤ Gn,s ∀n, s, t (4.3)

The maximum producible energy per hour in each installed unit of the renewable gen-erators depends on the current weather conditions, which is expressed as an availability

47


gn,s,t per unit of its capacity:

0 ≤ gn,s,t ≤ gn,s,tGn,s ∀n, s, t (4.4)

Note that excess energy can always be curtailed, e.g., by pitch regulation of wind turbinesor spillage in hydro power plants. Only reservoir hydro power plants can delay the dispatchof the natural inflow to some extent by utilizing the storage reservoir.

The installed capacity itself is also subject to optimisation, with a maximum limit Gmaxn,s

set by the geographic potential:

0 ≤ Gn,s ≤ Gmaxn,s ∀n, s (4.5)

The capacity Gn,s and the final dispatch gn,s,t of each generator are determined in theoptimisation such that they respect the physical constraints above, while minimising thetotal costs summed in the objective function (4.1).

4.2.4 Storage operation

The state-of-charge socn,s,t of all storage units has to be consistent with the charging anddischarging in each hour, and less than the storage capacity

socn,s,t = socn,s,t−1 + η1gn,s,t,charge − η−12 gn,s,t,discharge

+ gn,s,t,inflow − gn,s,t,spillage , (4.6)

0 ≤ socn,s,t ≤ hs,max ·Gn,s ∀n, s, t (4.7)

The efficiencies η1, η2 determine the losses during charging and discharging, respectively.These losses also imply that the storage is only charged when there is oversupply of poweravailable in the system, and discharged when the generators can not produce enoughpower and the import options are not sufficient. The state-of-charge is limited by theenergy capacity En,s = hs,max · Gn,s. Here, hs,max is the fixed amount of time in whichthe storage unit can be fully charged or discharged at maximum power. In this model,reservoir hydroelectricity storage can be charged by natural inflow of water, which has tobe spilled should the reservoir already be full in a given hour.

The state-of-charge is assumed to be cyclic, i.e., it is required to be equal in the first andthe last hour of the simulation: socn,s,t=0 = socn,s,t=T . This is reasonable when modellinga full year, due to the yearly periodicity of demand and seasonal generation patterns, andallows efficient usage of the storage at the beginning of the modelled time range.

4.2.5 Inter-connecting transmission

The transmission lines between countries are treated as a transport model with controllabledispatch (a coupled source and sink), constrained by energy conservation at each node.This is considered to be a justifiable approximation because many of the internationalconnections are already controllable point-to-point HVDC connections, such as those un-dersea (like France-Britain), those over land (like the Spain-France INELFE project) orthose in the planning phase (like the HVDC link planned between Germany and Belgium),while the flow on borders with only HVAC connections are being increasingly controlled byphase-shifting transformers (like the German-Dutch, German-Polish and German-Czech

48

4.2 Methods: Model

borders). This also follows the way that interconnectors are handled in market clearingwith Net Transfer Capacities (NTCs) on many borders.

The absolute flows on these transmission lines cannot exceed the line capacities due tothermal limits:

|f`,t| ≤ F` ∀ `, t (4.8)

The line capacities F` can be expanded by the model if it is cost-effective to do so. Tosatisfy n-1 security requirements, a safety margin of 33% of the installed capacity can beused [87, 70]. This can be emulated a posteriori by increasing the optimized NTCs by afactor of fn−1 = (1−margin)−1 = 1.5.

The lengths of the interconnecting transmission lines l` are set by the distance betweenthe geographical mid-points of each country, so that some of the transmission within eachcountry is also reflected in the optimisation. A factor of 25% is added to the line lengths toaccount for the fact that transmission lines cannot be placed as the crow flies due to landuse restriction. It is assumed that there is sufficient grid capacity within each countryto redistribute power as necessary. This assumption is driven by the decision to focuson long-distance interconnecting transmission, which enables the leveraging of continen-tal smoothing effects of interest here, but the assumption may not always be reasonable,given that there are already North–South grid bottlenecks in Germany, for example. How-ever, many more spatially-detailed studies [70, 88] show that total transmission costs aretypically small compared to the total generation investment cost. The cost impact onlybecomes significant if the internal transmission lines cannot be built because of missingpublic acceptance, which then drives up generation costs if the best sites cannot be ex-ploited. This trade-off is the subject of a forthcoming paper [89].

The sum of transmission line capacities multiplied by their lengths is restricted by a capCAPLV which is varied in different simulations:∑

`

l` · F` ≤ CAPLV ↔ µLV (4.9)

Line capacities are weighted by their lengths because the length increases both the costand public acceptance problems of the transmission lines. The cap, measured in MWkm,was raised from zero to the point where the constraint was no longer binding. The KKTmultiplier, or shadow price, µLV indicates the marginal value of an increase in line vol-ume LV to the system; it can also be interpreted as the cost per MWkm necessary forthe optimal solution to have the transmission volume CAPLV if the constraint (4.9) isdeactivated.

4.2.6 CO2 emission constraints

CO2 emissions are also limited by a cap CAPCO2 , implemented using the specific emissionses in CO2-tonne-per-MWh of the fuel of generator type s and the efficiency ηs of thegenerator: ∑

n,s,t

1

ηsgn,s,t · es ≤ CAPCO2 ↔ µCO2 (4.10)

The KKT multiplier µCO2 indicates the carbon dioxide price necessary to obtain thisreduction in emissions in an unconstrained market.

49


4.2.7 Software implementation

The model was implemented in the PyPSA [83] modelling framework and was optimisedusing the logarithmic barrier algorithm of the Gurobi [90] solver software. Using thisalgorithm the model typically solves in 1−2 hours per scenario on the local compute node(which has multiple Intel Xeon CPU cores rated at 2.3 GHz and 128 GB of RAM). Thisprovides solutions whose accuracy can be measured by the closeness of the duality gap,which in all simulations was at most 2 · 10−6 of the total objective value.

4.3 Methods: Data

The data underlying this model is presented in this section.

4.3.1 Network Topology

Following [68], the model consists of 30 nodes with one node per country of the EU-28, excluding Cyprus and Malta, but including Norway, Switzerland, Serbia, and Bosniaand Herzegovina. The nodes are connected with the topology of the already existinginternational transmission lines (see Fig. 4.4 for the topology).

4.3.2 Time series

The model is run for a full year with hourly resolution. The year 2011 was chosen because itis the earliest available year with full availability of the input data. The hourly electricitydemand in each country is based on [28, 52]. The onshore wind, offshore wind, andsolar photovoltaic (PV) power generation are based on historic weather data with hourlytemporal and a 40 × 40 km2 spatial resolution over Europe using a similar method asdescribed in [50, 91]. This method first converts weather data to potential power generationtime series in each raster cell and then aggregates the results on country level, weightedby a spatial distribution of generators. This sets the availability gn,s,t per unit of capacityof the renewable generation (cf. (4.4)).

4.3.3 Capacity layouts

The capacity layouts of the three renewable resources in each country were set proportionalto the usable area and the potential full load hours per raster cell, such that sites withhigher average power production are preferred and the average full load hours are relativelyhigh. The available area was restricted by the following constraints: Onshore wind and PVcan only be built in areas with certain land use types defined by the CORINE database[92], following the selection reported by [65]. Therefore, wind farms are not placed inurban areas and solar panels are not built in forests, for example. Offshore wind siteswere restricted to a maximum water depth of 50 m. Additionally, all nature reserves andrestricted areas defined in the Natura database [93] are excluded. Note that this sourcedid not include such data for non-EU-28 countries, and therefore possible restrictions inthese countries are not considered in this study.

Fig. 4.1 indicates that the spread of potential full load hours of onshore wind is largein large countries. The average full load hours are an important factor in determiningthe spatial distribution of installed capacity. If the distribution of full load hours is very

50

4.3 Methods: Data

0

1

2

3

4

5

6

7

8

9

wind average power density [GWh/a/km

2]

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

solar average power density [GWh/a/km

2]

Figure 4.1: Potential average power density for installable wind (left) and solar (right) generationper ∼ 40× 40km2 raster cell over Europe, once various land use restrictions have been taken intoaccount. Raster cells with zero values and areas outside the considered regions are white.

inhomogeneous, the average depends strongly on the region size after determining thecapacity layout as described above. In order to get a better estimate of the economicefficiency of wind turbines in each country and to allow a fair comparison between countriesof different sizes, we split the onshore wind layout of the ten largest countries into up tofour equal area parts. The spatial distribution of the new parts in each country is definedby similar full load hours. This procedure increases the spatial resolution of the onshorewind generation by adding independent classes of generators with different time series andaverage full load hours to the single node of a country. Their optimized capacities andproduced energies are later aggregated again on country level for analysis.

4.3.4 Geographic potential

The geographic installation potential Gmaxn,s is also based on these layouts. It is assumedthat in each country each renewable capacity can be extended proportional to this layoutonly until the installation density reaches a threshold somewhere. The maximum instal-lation density of both onshore and offshore wind power is assumed to be 10 MW/km2

[65]. Additionally, it is assumed that only a 20% fraction of the already restricted area isavailable for installation of wind generators due to competing land use and likely publicacceptance issues. This leads to an effective threshold of 2 MW/km2. For the same rea-sons, only up to 1% of the area can be used for solar PV panels with a nominal capacityof 145 MW/km2 [91]. This results in a potential installable energy density per raster cellthat is shown in Fig. 4.1. Most of the best wind conditions are located along the NorthSea, the Baltic Sea, and the Aegean Sea, while the highest solar potentials are in Spainand south-east Europe.

4.3.5 Hydroelectricity

Reservoir hydro and run-of-river power plants can convert water inflow into electricity.Both generation types are assumed to remain at their currently installed capacity, i.e., arenot expanded, due to environmental concerns, which defines a conservative lower bound.Data on country-specific installed hydro power capacities is provided by [94, 95], but does

51


not distinguish between reservoir and run-of-river types. Therefore, the power capacitieswere split proportional to the run-of-river share per country published by [96]. Thissource did not report run-of-river shares for some countries, in which case the estimatedshares collected within the Restore2050 project [94] were taken instead. All energy storagecapacities from [94] are attributed to the reservoir hydro power plants, for a total of 207.6TWh.

The inflow time series per country are based on [94], where daily river run-off data[97] was weighted by the respective geographic height and normalized to match yearlygeneration data. The total inflow in each country was split into reservoir and run-of-riverinflow, proportional to the shares of installed power capacity.

4.3.6 Non-renewable generators

The renewable generator portfolio in each country can be complemented by conventionalbackup generators. Their global annual energy generation is limited by a strict EuropeanCO2 emission limit corresponding to a reduction of 95% compared to 1990, but they canbe dispatched independent of weather conditions and therefore help to provide sufficientpower even in the most extreme hours. The conventional backup system is representedhere by open-cycle gas turbines (OCGT), following the assumptions of [60], due to theirhigh flexibility and load-following capabilities, and relatively low capital costs, such thatthey require few full load hours per year to be economically feasible.

4.3.7 Storage

Fluctuating generation can also be mitigated to some extent via temporal shifting instorage units. In this study, three types of storage technologies are considered: pumpedhydro storage (PHS), central batteries, and hydrogen (H2) storage with electrolyzers, fuelcells, and above-ground steel tanks [61]. All three storage types are modelled with equalnominal charging and discharging power capacities, respectively. Storage and dispatchefficiencies may differ, however, as listed in Table 4.1. The storage energy capacitiesare assumed to be proportional to the power capacities such that a storage unit canbe fully charged or discharged at maximum power in a fixed amount of time hs,max.These simplifications are done to limit computational effort and partly due to lack ofdetailed publicly available data. The storage energy standing loss over time is not explicitlyincluded in the model.

The already existing pumped hydro storage capacities reported by [94] are assumed toremain in use, but without additional extension potential. This assumption is slightlyconservative, but further PHS potentials in Europe are estimated to be small due toenvironmental concerns. Capital costs for existing units are neglected due to the longtechnical lifetimes and site-specific investment contingencies of hydro power plants. PHSunits are typically designed to provide short term load shifting within a day. Assuming anappropriate dimensioning of storage energy capacity, the latter is set via hPHS,max = 6 h.

The installation potential of batteries and H2 storage is not constrained. Central batter-ies have high round-trip efficiencies but relatively high storage losses over time. Therefore,they are best suited for short-term storage, and are modelled here with hbattery,max = 6 h.H2 storage can provide a long-term storage option due to relatively low efficiencies butlow losses over time. A relatively large energy capacity is chosen with hH2,max = 168 h,

52

4.3Meth

ods:

Data

Table 4.1: Input parameters based on 2030 value estimates from [60] unless stated otherwise.

Technology investment fixed O&M marginal lifetime efficiency capital cost per hmax(AC/kW) cost cost (years) (fraction) energy storage (h)

(AC/kW/year) (AC/MWh) (AC/kWh)

onshore wind 1182 35 0.015a 25 1offshore wind 2506 80 0.02a 25 1solar PV 600 25 0.01a 25 1OCGTb 400 15 58.4c 30 0.39hydrogen storaged 555 9.2 0 20 0.75 · 0.58e 8.4 168central battery (LiTi)d 310 9.3 0 20 0.9 · 0.9e 144.6 6transmissionf 400 AC/MWkm 2% 0 40 1PHS 2000g 20 0 80 0.75 N/Ag 6hydro reservoir 2000g 20 0 80 0.9 N/Ag fixedh

run-of-river 3000g 60 0 80 0.9

a The order of curtailment is determined by assuming small marginal costs for renewables.b Open-cycle gas turbines have a CO2 emission intensity of 0.19 t/MWth.c This includes fuel costs of 21.6 AC/MWhth.d Budischak et al. [61].e The storage round-trip efficiency consists of charging and discharging efficiencies µ1 · µ2.f Hagspiel et al. [69].g The installed facilities are not expanded in this model and are considered to be amortized.h Determined by size of existing energy storage [96, 94].

53


Table 4.2: Optimized average system costs in [AC/MWh] for the allowed total interconnecting linevolume of the zero, today’s, compromise, and optimal grid scenarios. Also given are the overallaverage local marginal prices (LMP) and the total line volume.

Scenario Zero Today Comp. Opt.

Line vol. [TWkm] 0.0 31.25 125.0 285.70

battery storage 9.9 8.5 4.5 1.7hydrogen storage 8.1 5.4 3.4 3.1gas 4.6 4.2 4.1 4.5solar 26.1 21.8 14.7 9.4onshore wind 22.3 20.3 23.4 28.6offshore wind 10.8 12.0 11.4 7.5transmission lines 0.0 1.0 3.6 7.6PHS 0.3 0.3 0.3 0.3run-of-river 1.4 1.4 1.4 1.4reservoir hydro 0.8 0.8 0.8 0.8

Total cost 84.1 75.7 67.5 64.8

Avgerage LMP 116.5 107.5 97.4 90.1

i.e., one week.

4.3.8 Cost assumptions

All cost assumptions are summarized in Table 4.1. The given overnight capital costs wereconverted to net present costs with a discount rate of 7% over the economic lifetime.

No expansions of hydro reservoir, run-of-river, and pumped hydro storage capacitiesare considered in this study and the already existing facilities are considered amortized.Therefore, only their fixed operation and maintenance (O&M) costs are taken into accountwhen calculating the total system cost.

The transmission investment per line ` is calculated as: (400AC/kW/km·1.25l`+cCP )fn−1

with converter pair costs cCP = 150000AC/MW, and n-1 security factor fn−1 = 1.5.The fixed operation and maintenance costs for transmission lines are 2% of the (length-dependent) investment cost.

4.4 Results

4.4.1 Total costs as function of line volume constraints

Fig. 4.2 shows the composition of the average cost for all investment and operation ofthe optimized highly-renewable European system as a function of the allowed volume oftransmission lines (set by the cap in equation (4.9) and measured in MWkm). In thisgraphic transmission costs are set assuming the costs for overhead lines are used. Theresults are also given in Table 4.2.

Note first that the development of the costs is highly non-linear as transmission volumeis reduced. As the volume is restricted from the optimal point, the costs barely increase; at

54

4.4 Results

0 50 100 150 200 250 300Allowed interconnecting transmission volume [TWkm]

0

20

40

60

80

100

120

Av

era

ge

sy

ste

m c

ost

[E

UR

/MW

h]

today'sgrid

compromisegrid

optimalgrid

battery storage

hydrogen storage

gas

solar

onshore wind

offshore wind

transmission lines

PHS

run-of-river

reservoir hydro

Figure 4.2: Optimized average total system costs per unit of generated energy in AC/MWh asfunction of the allowed total line volume between zero transmission and the cost optimal vol-ume. The total costs are divided into costs for the modelled components battery storage (grey),H2 storage (magenta), gas (red), solar (yellow), onshore wind (blue), offshore wind (cyan), andtransmission lines (black), top to bottom. The dashed vertical lines mark the transmission linevolumes of today’s grid (red), the compromise grid (green) at four times today’s volume, and theeconomically optimal grid (black). Larger allowed line volumes cannot add value.

this point the solution space is very flat, i.e., costs are insensitive to restricting transmissionexpansion. Only when the transmission volume is restricted to a few multiples of today’sgrid2, the costs start to increase very steeply, driven by bigger investments in storagetechnologies and solar power.

In the economically optimal scenario, the total average cost for a highly renewable powersystem is 64.8 AC/MWh. For comparison the cost of today’s European system can be esti-mated from the currently installed net generation capacities and yearly energy generationfor 2013 [98] combined with technology cost assumptions from the same source [60] asbetween 52 and 61 AC/MWh, depending on whether the decommissioning and waste dis-posal costs for nuclear power are included. This indicates that highly renewable scenarioscan have system costs that are comparable to today’s system cost. In these estimates,potential CO2 emission prices are neglected, which would predominantly increase costs inthe conventional system. Although transmission investments contribute only 12% to thetotal cost, the optimum line volume is 286 TWkm, roughly 9 times higher than today’sNTCs of 31 TWkm.

Such a large grid extension seems to be infeasible due to social acceptance issues [71].On the other hand, restricting transmission requires more storage to deal with variability,driving up the costs by up to 30% compared to the economic optimum. However, thecost development between these two extremes is not linear: most of the increase occurs atsmall allowed line volumes, while the cost curve is quite flat closer to the optimum. Thisallows a compromise grid of four times today’s NTCs to lock in 85% of the cost reduction

2Today’s grid is taken to be the Net Transfer Capacities (NTCs) between countries, multiplied by theline lengths defined in the model.

55


of the optimally extended grid compared to the case without transmission grid, giving anaverage cost of 79.9 AC/MWh. Today’s line volume, optimally distributed, would lock injust 43% of the benefit.

If the composition of costs is examined, wind power installations contribute around 32 to36 AC/MWh to the average system cost, relatively independent of the allowed transmissionvolume. For high line volumes, this is the dominant part of the cost and reflects the factthat most of the energy is generated by wind. However, only the cost share of onshorewind increases roughly linearly from 22.3 to 28.6AC/MWh with interconnection volumewhile the offshore wind share decreases accordingly. The non-linear reduction of the totalsystem costs is due to the decreasing contributions of solar, batteries, and H2 storage. Allthree show a similar behaviour of a strong decrease at low transmission volumes that levelsoff towards the optimal grid volume. Solar costs account for a third of total cost at firstbut add only 9.4AC/MWh in the optimal case. The cost share of batteries and H2 storageis relatively small with respectively up to 9.9 and 8.1AC/MWh, and in the economicallyoptimal scenario almost no batteries are installed.

Onshore wind is the only system component whose cost share increases with transmissionvolume. Weather patterns over Europe are typically correlated over synoptic spatial scalesof roughly 1000 km, such that there are usually a few independent wind regions at alltimes. European-wide transmission therefore allows direct power balancing between theseregions, which increases the efficient use of the wind generators. In contrast, solar PVprofits much less from this smoothing effect because one of its dominant variabilities isdue to the day-night cycle that affects all of Europe almost at the same time. Transmissionalso allows the sites with higher capacity factors to be exploited more fully, which furtherincreases efficiency.

However, if transmission is strongly limited, most power balancing must be done locallywith the help of storage or, if available, dispatchable sources. Wind power is less effectivein this case because the wind pattern typically vary on a time scale of 3 to 10 days. Shiftingthe demand over such periods requires large amounts of energy storage capacity, e.g., fromlong-term hydrogen storage. It is therefore cost effective to install a larger share of solar,where the energy often has to be stored only between day and night.

Additionally, increasing the transmission volume allows to share temporarily unused andlong-term storage between countries, which makes them more cost efficient and can help toreduce the installation demand. It also enables better access to the existing dispatchableand pumped hydro power facilities that are mostly located in Scandinavia and the Alps.

Offshore wind has the least volatile generation and can therefore provide relatively con-tinuous power also to neighbouring countries and has the least storage needs. This isbeneficial as long as line volumes are restricted, but due to the high investment costs ofoffshore wind, it is gradually replaced by a combination of less capital-intensive onshorewind generation and smoothing via an extended grid. For very small line volumes, off-shore exports are also limited by grid congestion, which leads to a slight reduction ofinstallations.

The costs for the three types of hydro power is determined by the fixed operationand maintenance cost of their assumed installation capacities and was not subject to theoptimization. They are therefore constant at 2.5 AC/MWh throughout all scenarios.

The average costs obtained here are similar to values from the literature. For exam-ple, Czisch [64] used similar cost assumptions (with the exception of the then-reasonableovernight cost of 5500 AC/kW for PV) and a target of 100% CO2-free generation and found

56

4.4 Results

Table 4.3: Optimized annual energy generation in [%] of the annual energy demand for the allowedtotal interconnecting line volume of the zero, today’s, compromise, and optimal grid scenarios.

Scenario Zero Today Comp. Opt.

Line vol. [TWkm] 0.0 31.25 125.0 285.70

gas 5.1 5.1 5.1 5.1solar 40.1 34.9 24.6 16.2onshore wind 37.2 37.4 46.6 59.0offshore wind 13.8 15.6 13.9 8.6run-of-river 4.9 5.0 5.0 5.0reservoir hydro 9.5 10.0 10.0 10.0

Total energy 110.6 108.0 105.2 104.0

average costs of 46.5 AC/MWh for optimal transmission in a system comprising Europe,the Middle East and North Africa (EUMENA), 52 AC/MWh with no transmission betweenAfrica and Europe, and 80 AC/MWh with no transmission at all between countries. Scholz[65] found for a 100% renewable system for EUNA an average cost of 69 AC/MWh withoptimal transmission and 83 AC/MWh with no transmission. Bussar et al. [74] found forEUMENA an optimal cost of 69 AC/MWh and a total line volume of 375 TWkm withoptimal transmission. These costs compare well to the extreme points of our analysis.Analysing the full spectrum of possible network extensions between the extreme points,as has been done here, reveals the non-linear development of the costs and the benefits ofa compromise transmission expansion.

4.4.2 Energy mix

The composition of energy generation per year in units of the total demand 3152 TWh/aas a function of transmission line volume is shown in Fig. 4.3 and Table 4.3. The energymix is dominated by wind which contributes 46% to 65% of the generation, mostly fromonshore generators. Its share increases with the line volume as large scale wind variationscan be smoothed better by a larger grid. This is consistent with the trends alreadyindicated by the cost analysis. The large contribution from wind relative to the cost shareshows an efficient utilization of the installed capacity. The amount of energy contributedby solar PV generation is relatively high with 40% of the demand as long as transmissionis strongly restricted, but decreases to only 16% with optimal grid extension.

There is a clear correlation between the share of solar generation and the excess produc-tion required to compensate losses from storage. The latter is indicated by values above 1in Fig. 4.3. It decreases with allowed interconnection from 11% to 4% of the demand. Thisindicates that systems with a lack of transmission require a more diverse energy mix withrelatively high shares of solar generation and storage use, while additional transmissionincreases both the economic and energy efficiency.

The constant contribution from run-of-river and reservoir hydro of 15% of the demandis equal to the inflow and indicates a negligible need for spillage. The energy from gaspower plants is limited by CO2 emission constraints to 5.1% of the demand in all cases.

In hours with potential excess variable renewable generation that can neither be con-

57


0 50 100 150 200 250 300Allowed interconnecting transmission volume [TWkm]

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Energy generation / demand

gas

solar

onshore wind

offshore wind

run-of-river

reservoir hydro

Figure 4.3: Optimized annual dispatched energy generation in units of the annual energy demandas function of the allowed total line volume. The total energy is divided into generation from themodelled components gas (red), solar (yellow), onshore wind (blue), offshore wind (cyan), run-of-river (light green), and reservoir hydro (green), top to bottom. As in Fig. 4.2, the dashed verticallines mark the transmission line volumes of today’s grid (red), the compromise grid (green) at fourtimes today’s volume, and the economically optimal grid (black). Energy generation above thedemand is caused by losses from storage use. The amount of curtailed energy is not shown.

sumed or stored, this energy is curtailed. The total curtailed energy is reduced from 11%of demand (340 TWh/a) with no transmission to 9% of demand (286 TWh/a) with op-timal transmission. There is an inherent ambiguity in the order of curtailment betweengenerators with equal, i.e., zero marginal costs. This ambiguity was lifted by introducingdifferent small costs for each generator type (see Tab. 4.1). Offshore wind generation hasthe highest marginal cost and is curtailed first, followed if necessary by onshore wind,solar, and finally run-of-river generation. Therefore, the contributions from run-of-riverand solar are as high as possible. This introduces a bias in the mix of produced energy.However, this bias does not affect the installed capacities and system costs, but only re-distributes the effective full load hours. In practice, a suitable reimbursement mechanismfor curtailing could easily limit the economic consequences. The curtailment order can bejustified by practical manageability considerations: it is easier to curtail the same amountof power in a few large off-shore wind parks than a large number of decentral solar panels.

4.4.3 Spatial distribution of infrastructure

The spatial distributions of the optimized annual costs for generation, storage and trans-mission are shown in Fig. 4.4 for the three scenarios of allowed transmission line volumeof no transmission, the compromise grid expansion, and the economically optimal grid.The same data is graphed in Fig. 4.5 for ease of comparison, normalised to the averageload in each country. In Fig. 4.6 the total energy generation is plotted, normalised by eachcountry’s demand.

First we consider the case without transmission grid. Although this case is unrealisticgiven that countries are already inter-connected today, it provides a useful reference pointto assess the benefits of cooperation. Without transmission grid, there is a very diverse

58

4.4 Results

Line volume = 0 TWkm

Transmission lines (= 10 GW)

Annual cost (= 5.0e9 Euro/a)







run-of-river

reservoir hydro

PHS

battery storage

hydrogen storage

gas

solar

onshore wind

offshore wind

Figure 4.4: Distributions of the cost composition per country as pie charts for the case of zerointerconnecting transmission (top), compromise grid (middle), and economically optimal transmis-sion (bottom). The color code is the same as in Fig. 4.2. The area of the circles is proportional tothe total costs per country. The modelled international transmission lines are shown as black lineswith width proportional to their optimized net transfer capacity.

59


AT

BA BE

BG

CH

CZ

DE

DK EE

ES FI FR GB

GR

HR

HU IE IT LT LU LV NL

NO PL

PT

RO RS

SE SI

SK

country

0

50

100

150

200

250

300

350

400

450

Loca

l sy

stem

cost

[EUR/M

Wh] battery storage

hydrogen storage

gas

solar

onshore wind

offshore wind

PHS

run-of-river

reservoir hydro

Figure 4.5: Generation and storage costs normalised by annual demand for each country. Theleft, middle, and right bars are for the zero, compromise, and optimal transmission scenarios,respectively. Energy generation can be above the local demand due to storage losses and exports.The color code is the same as in Fig. 4.3. The 30 modelled countries are ordered alphabetically bytheir ISO2 code.

AT

BA BE

BG

CH

CZ

DE

DK EE

ES FI FR GB

GR

HR


NO PL

PT

RO RS

SE SI

SK

country

0

1

2

3

4

5

6

7

Energy generation / demand gas

solar

onshore wind

offshore wind

run-of-river

reservoir hydro

Figure 4.6: Energy generation in units of demand per country split by generator type. Theleft, middle, and right bars are for the zero, compromise, and optimal transmission scenarios,respectively. Energy generation can be above the local demand due to storage losses and exports.The color code is the same as in Fig. 4.3.

60

4.4 Results

mix of energy sources where almost every country has wind, solar, and gas generation,with the highest shares of solar in southern Europe. This technological diversification iscost-effective in the absence of transmission because the different resource characteristicson different time scales can be used for some country internal balancing, as discussed,e.g., by [68]. However, this still requires significant amounts of storage in most countries,with a relatively homogeneous share of around 20% of the costs, similar to its share ofthe total costs as shown in Fig. 4.2. The mix of H2 and battery storage especially in thecentral European countries reflects the composition of generation technologies: countrieswith high shares of wind power have high shares of longer-term H2 storage, while solardominated countries usually have larger, or exclusively, shorter-term battery capacities.The existing pumped hydro storage units have properties similar to those of batteries andalso allow a slightly increased share of solar generation.

The dispatchable reservoir hydro power is highly beneficial where available by providinga flexible source of energy that can be stored until needed. This helps to balance themismatch between fluctuating renewable generation and demand and can reduce costsconsiderably. Countries with large hydro capacities like Norway and Switzerland have tobuild relatively little other infrastructure.

Offshore wind power often has high capacity factors and relatively little volatility buthigh installation costs. Ten countries also utilize their offshore wind resources in thisscenario. In Greece, the Netherlands, and Germany the investment shares are above25%. It is not built in Great Britain, Ireland, and Denmark which have some of the bestoffshore wind efficiencies, but also very good onshore wind conditions and large installationpotentials. There, long term H2 storage and the differing characteristics of solar providemore benefits than additional offshore wind.

In the scenario with the compromise grid expansion, there is already some splittingof resource utilization between different regions in Europe in order to better exploit theavailable potentials. Due to relatively weak solar irradiation in northern Europe, solargeneration is no longer built there, which also largely removes the benefits of battery stor-age in this region. Instead, only a few countries like Denmark, Great Britain, and Norwaywith very good wind potentials increase the size of their onshore wind installations andexport the excess energy. It is then cost efficient for the other countries to install similaramounts or even less onshore wind capacity than in the scenario without transmission.The grid infrastructure is built predominantly between large and wind dominated coun-tries in north-western Europe, where it helps to increase the generation efficiency furthervia synoptic-scale spatial smoothing of wind fluctuations. This also reduces the need for H2

storage in all countries with wind installations. Only Denmark and Great Britain increasetheir H2 storage capacities slightly, which suggests that their exports can be supported bycongestion management through storage.

In south-eastern Europe, the solar and battery installations are almost the same asin the previous scenario, but the introduction of relatively small transmission capacitiesallows to replace the local wind installations with imports from nearby regions. Exceptionsare Greece and Romania that have access to good offshore wind resources, that are nowutilized even more in Greece and used for exports.

The technology mix especially in the larger countries in central and south-western Eu-rope is still heterogeneous due to compromises between resource efficiency and transmissionconstraints. This is also indicated by the concentration of balancing power generation fromgas power plant in central Europe.

61


AT

BA BE

BG

CH

CZ

DE

DK EE

ES FI FR GB

GR

HR


NO PL

PT

RO RS

SE SI

SK

country

0

50

100

150

200

Local marginal price [EUR/MWh]

Allowed interconnecting transmission volume [TWkm]

0 125 286

Figure 4.7: Average marginal prices at each node for the zero (purple), compromise (green) andoptimal (black) transmission scenarios.

For the case of economically optimal line volumes, there is a strong transmission gridexpansion over all of Europe that allows to balance synoptic-scale weather variations andfor optimal utilization of the best resource locations, making the trends discussed abovemore pronounced. This large grid allows significant net exports of onshore wind generationfrom a few countries like Denmark, Great Britain, Ireland, Norway, and Sweden. The firsttwo of these are located slightly more centrally in the grid and require less H2 storage thanin the previous scenario, while the latter three are further away from the importers, andbuild more H2 storage.

The solar generation is concentrated in southern Europe where the highest solar fullload hours are found, but still require net imports. The South-East has the smallest gridexpansion, indicating that solar generation does not directly profit as much from (local)spatial smoothing effects. Greece plays an important role in this region to diversify thepower sources with its high share of offshore wind that can be exported, e.g., during thenight.

4.4.4 Marginal prices

The average marginal prices for each node derived from the KKT multipliers λn,t in equa-tion (4.2) are plotted in Fig. 4.7 for each node and for three scenarios. Here several trendsare noticeable. First, the overall prices decrease as transmission is increased, reflecting thedecrease in total system costs. The spread of prices between the nodes also narrows asincreased transmission reduces congestion, allowing prices to equalise within the network.Finally we see that the overall prices are slightly higher than the average system costs,because they include the scarcity costs induced by the constraints, such as the CO2 costwhich contributes on average 5 AC/MWh and the scarcity costs of generation sites withlimited expansion potential.

The lowest prices are in those countries with high shares of zero-marginal-cost renewablegeneration, such as Denmark, Ireland, Sweden and Norway. Norway actually sees anincrease in prices as transmission is expanded, since it can share its abundant hydroresources with other countries, to the benefit of the entire system.

62

4.4 Results

0 100 200 300 400 500Allowed interconnecting transmission volume [TWkm]

0

1000

2000

3000

4000

5000

6000

Shadow price [EUR/MWkm

]

today'sgrid

optimalgrid

overheadlines

compromisegrid

undergroundcable

Line extension shadow price

Figure 4.8: Shadow price of the line volume constraint in units of overnight capital costs asfunction of the allowed total line volume. As in Fig. 4.2, the dashed vertical lines mark thetransmission line volumes of today’s grid (red), the compromise grid (green) at four times today’svolume, and the economically optimal grid (black). The dotted horizontal lines indicate the capitalcosts of overhead transmission lines (black) and underground cables (green).

4.4.5 Line volume shadow price

The economic value of transmission line volumes can be analyzed with the help of theshadow price µLV of the line volume constraint defined in eq. (4.9). The shadow price isthe dual variable of this constraint and can be interpreted as the price per unit of linevolume the system is willing to pay to build a given amount LV of constrained line volume.In other words, this is the cost required so that in an unconstrained market, the economicoptimum is to build a total line volume of LV .

Therefore, at the assumed current costs for over-land HVDC transmission lines of400 AC/MWkm, the model finds the optimal grid volume of 286 TWkm, as marked bythe black lines in Fig. 4.8. Here, the plotted shadow price is defined such that it rep-resents the overnight capital costs of lines. This figure allows to read off the points atwhich more expensive transmission solutions, such as underground cabling, make eco-nomic sense. If all lines would be replaced by underground cables with a current cost ofca. 2000 AC/MWkm, a grid extension to 90 TWkm, roughly three times the current NTCwould still be economically optimal in this model. The proposed compromise grid withfour times today’s volumes derived from considerations of the total system costs would stillbe built if transmission would cost 1300 AC/MWkm. In a purely market based solution,transmission would have to cost 4000 AC/MWkm in order to limit the optimal line volumeto today’s NTC in this model.

4.4.6 Dispatch time series

In this subsection some example dispatch time series from the model are examined. Fig. 4.9shows an example from France in August with high generation from both wind and solar.Some onshore and offshore wind has to be curtailed, as shown by the difference betweenavailable power (dashed lines) and dispatched power (solid lines). More offshore than

63


onshore wind is curtailed, but no solar generation, following the assumed curtailmentordering via marginal costs as described above.

During this period, hydrogen storage is charged at full power most of the time whenthere is excess wind generation, and is only discharged in a few nights with very littlewind generation. Similarly, reservoir hydro is also only dispatched during these nightsand accumulates the inflow the rest of the time, which is not shown here. Batteries andpumped hydro storage (PHS) provide peak shaving between day and night, where they arecharged mostly from solar during the day and discharge during the night. The imports andexports tend to be correlated with local under- and overproduction of wind, respectively,but they also depend strongly on the state of the rest of the network. The dispatch ofrun-of-river is almost constant and very small, and gas power is not generated during thistime.

Fig. 4.10 shows the behaviour of the state of charge for all the storage in Europe,revealing the different temporal scales on which each technology operates. Reservoir hydroshows a seasonal pattern, discharging in winter when demand is high, and charging inspring and summer as snow melts in mountainous areas. The sum of reservoir storage levelsnever drops to zero because it is aggregated over several countries; individual countriesdo drop to zero, but at different times. Hydrogen storage varies on seasonal and synopticscales, reflecting the pairing of this long-term storage with wind. Finally, battery andPHS show a daily pattern reflecting the use of this storage resource to balance variationsin solar generation.

4.5 Discussion

4.5.1 Comparison to the literature

Average system costs range in this study from 64.8 AC/MWh in the case of optimal trans-mission up to 84.1 AC/MWh with no inter-connecting transmission. These values are con-sistent with other values found in the literature. For example, Czisch [64] used similar costassumptions (with the exception of the then-reasonable overnight cost of 5500 AC/kW forPV) and a target of 100% CO2-free generation and found average costs of 46.5 AC/MWhfor optimal transmission in a system comprising Europe, the Middle East and NorthAfrica (EUMENA), 52 AC/MWh with no transmission between Africa and Europe, and80 AC/MWh with no transmission at all between countries. Scholz [65] found for a 100%renewable system for EUNA an average cost of 69 AC/MWh with optimal transmission and83 AC/MWh with no transmission. Bussar et al. [74] found for EUMENA an optimal costof 69 AC/MWh and a total line volume of 375 TWkm with optimal transmission. Thesecosts compare well to the extreme points of our analysis. Analysing the full spectrum ofpossible network extensions between the extreme points, as has been done here, revealsthe non-linear development of the costs and the benefits of a compromise transmissionexpansion.

In [68, 49] similar non-linear effects of transmission were found in a more simplifiedmodel of a highly renewable European electricity system without a limit on CO2 emis-sions, without storage or hydroelectricity, and without optimising transmission and gen-erator capacities. In that model, if there were no constraints on transmission, the modelwould build 12 times today’s inter-connecting capacities to minimise the need for backupenergy; however, 90% of the benefit was found with 4 times today’s capacities and 70% of

64

4.5 Discussion

0

20

40

60

80

100

120

Pow

er

[GW

]

gassolaronshore windoffshore wind

run-of-riverAvailableDemand

05Aug2011

06 07 08 09 10 11 12 13−30

−20

−10

0

10

20

30

Pow

er

[GW

]

battery storagehydrogen storage

PHSreservoir hydro

Import

Figure 4.9: Example time series of the optimized hourly dispatch of the different technologiesin France based on historic demand and weather data from Aug 5 - 14 2011 in the scenario withtoday’s interconnecting transmission volumes. The actual and available hourly power outputsof generators are respectively shown as solid and dashed lines. Discharging of storage units isindicated by positive, charging by negative values. Positive values of the black solid line markimports into France, negative values mark exports. The thick brown line shows the demand. Notethe different y-scale for top and bottom panel.

65


Jan2011

Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0.0

0.2

0.4

0.6

0.8

1.0

1.2

Energy level of storage (norm

ed)

hydrogen storagereservoir hydro

Aug2011

08 15 22 290.0

0.2

0.4

0.6

0.8

1.0

1.2

Energy level of storage (norm

ed)

battery storagePHS

hydrogen storagereservoir hydro

Figure 4.10: Hourly total energy storage levels for the compromise grid scenario, normalized tothe storage energy capacity. Battery storage and PHS levels show a similar, predominantly dailypattern, leading to some visual overlap of the lines.

66

4.5 Discussion

the benefit with 2 times today’s capacities. In [73] this approach was extended to includeoptimisation of wind and solar capacity placement, but again the results are not compara-ble because CO2 emissions were not limited (which would translate into a limit on backupenergy from fossil fuels), and storage and hydroelectricity were not considered. However,the average system cost range found in [73] of 53 AC/MWh to 64.5 AC/MWh, depending onthe amount of transmission and the level of optimisation of generation capacities, is alsocomparable to the studies mentioned above.

Next we turn to studies that optimise grid capacity in Europe with more network nodes,so that transmission lines inside each country are also seen in the model. These modelstend to see a lower overall level of grid expansion at the cost-optimal level than studieswhich aggregate each country to a single node. For example, in [69] with a 200-nodemodel of Europe, the cost-optimal grid capacity for a 90% CO2 reduction in the electricitysector is around double today’s total capacity. Similar results can be found in [43, 67] withup to 83 nodes. Lower levels of grid expansion are seen when looking at lower levels ofrenewables in the near future [70, 88]. The dependence of electricity system optimisationresults on the level of spatial resolution (i.e. the number of network nodes) was studied indetail recently in [89], where it was also found that the cost-optimal level of grid expansionfor a 95% CO2 reduction was around 2-3 times today’s capacities when including country-internal transmission lines; using more expensive underground cables for the grid expansionresults in optimal networks that are only 30% to 60% bigger than today. Models that onlyinclude transmission lines between countries, like the one presented in this paper, showbigger network expansions because interconnectors have traditionally been weaker thanthe networks inside countries, given that the current interconnected system has evolvedslowly by combining national systems.

In common with all the studies mentioned above, the model presented here shows thedominance of wind power (up to 65% of total energy production) when transmissionexpansion is allowed.

4.5.2 Limitations of the study

As discussed above, one limitation of this study is that grid bottlenecks inside each countryare not considered in the model, since we chose to focus on the benefits of internationaltransmission. It was shown in [89] that while expanding the grid to resolve these country-internal bottlenecks might double transmission costs in the cost-optimal case, these costsare still less than 10% of total system costs. If national networks cannot be expandedbecause of acceptance problems, these bottlenecks cause additional costs by restrictinggeneration feed-in, forcing a shift from offshore wind expansion to more local productionfrom solar and storage.

In this study the costs of possible expansion of the distribution grid and the provision ofancillary services have not been considered. Studies which have considered the expansion ofthe distribution grid for high shares of renewables show that these costs range from around10% to 15% of total system costs [87, 99, 100]; taking account of ancillary services, such asvoltage control, frequency control, fault current provision and black-start capabilities havealso been shown to play only a secondary role in the total system costs [101, 102, 103].

Another limitation of this study is that synergies arising from coupling the electricitysector to other energy sectors, such as transport and heating, have been neglected. Afollow-up study to this one is being prepared that considers sector-coupling in a European

67


context. Preliminary results [82] show that the coordinated charging of battery electricvehicles can replace the role of stationary batteries in balancing solar variations, while thelonger-term variations of wind can be accommodated using Power-To-Gas and Power-To-Heat units in combination with thermal energy storage. This sector coupling can furtherreduce the need for inter-connecting transmission.

4.6 Summary and Conclusions

In this chapter a techno-economic model was implemented and optimised to examine theeffect of different levels of inter-connecting transmission on the costs of the Europeanelectricity system, assuming a reduction of CO2 emissions of 95% compared to 1990 levels.This model includes renewable energy generation from wind, solar and hydro power, andstorage systems such as pumped hydro storage, batteries, and hydrogen storage units.

We interpolate continuously between a cost-optimized level of inter-connecting trans-mission and no or limited inter-connection between European countries. We analyse theaverage system costs depending on different transmission volume levels. This reveals non-linear effects which are not visible in studies of isolated transmission scenarios [64, 65, 74];in particular, most of the economic benefits of transmission expansion can be locked inwith a more modest expansion than the optimal solution. An expansion to four timestoday’s inter-connection capacities already enables 85% of the cost savings of the optimaltransmission expansion (9 times today’s). This conclusion has important policy conse-quences, because it offers a compromise between the needs of the electricity system andlow acceptance of transmission grid expansion by the public.

With the cost-optimal level of transmission, the European electricity system can bebuilt with a total average system cost as low as 64.8 AC/MWh, comparable to the cost ofthe current system without CO2 pricing. This system uses a continent-wide transmissiongrid to balance the large-scale synoptic variations of wind (65% of energy generation)and integrate hydroelectricity from mountainous regions (15% of generation). Restrictingtransmission drives total costs up by a third, because the grid is no longer available tobalance the variations of wind in space. Instead, long-term hydrogen storage must be usedto balance the variations of wind over several days; since this is comparatively expensive,restricting transmission favours a combination of solar generation (up to 36%) with dailybattery storage. This shows the importance of considering spatial and temporal scaleswhen analysing the integration of renewables. It also shows that there is no single solutionfor a highly renewable electricity system. Instead there is a family of possible solutionswith different properties (such as level of transmission) and different costs.

This study has highlighted the importance and cost-efficiency of a global Europeanenergy transmission network, even if it can not be extended to its economically optimalsize due to external limitations like public acceptance issues. The flatness of the costsaround the optimal point as transmission is restricted is a general feature that also appliesto other types of restrictions. In a forthcoming study, this work will be extended to theexploration of other directions that also turn out to be flat in the optimization space, suchas restrictions on the import levels of each country, restrictions on onshore wind due topublic acceptance problems, and variations of the CO2 cap or price. These flat directionsare important, because they may allow solutions that are both cost-effective and also takeaccount of other political restrictions. In a further study, the benefits of coupling to other

68

4.6 Summary and Conclusions

energy sectors, such as transport and heating will be considered.These studies will lead to a much better understanding of the importance of European

cooperation in terms of energy distribution, and it will contribute to a more stable, cost-efficient and effective setting for the future stability of a highly renewable European energynetwork.

69

5 Sensitivity Analysis

5.1 Introduction

In the model that has been build up in the previous three chapters, there are intrinsicuncertainties in some of the assumptions applied to the parameters used to constrain themodel. These uncertainties originate from the fact that the assumptions are based on inputparameters that are sensitive to several external decisions. For example, constraints due topolitical decisions are difficult to predict over a longer time period, and a broad spectrumof possibilities for political decisions exists. Furthermore, economic cost assumptions aregenerally difficult to constrain as the cost estimates for current technologies already varystrongly in the literature, and thus the evolution of the costs is even more difficult topredict. Additionally, the physical input parameters are also subject to uncertainties, asthey depend on the historical weather data from just a single year (or in the best caseseven years) record, which is too short to capture the impact of extreme weather eventsand also might introduce a bias to the weather conditions that dominated the consideredtime period.

In this chapter, several parameters of the model will be varied to test the sensitivity ofthe results on the three aforementioned sources of uncertainties. This sensitivity analysiswill allow to understand the model in more detail, especially with respect to the corre-lations between the different implemented technologies. It will also allow to identify thecomponents which have the strongest influence on the complex interconnected system andpredict the variables that could best be used to optimize the model.

5.2 Sensitivity to policy constraints

5.2.1 Onshore wind potentials

In the previous chapter 4 the influence of external constraints on the transmission linevolume limit due to, e.g., policy considerations and public acceptance issues was discussedin detail. Another important component of the energy system, onshore wind turbines, hascaused acceptance issues in the past. The impact of an external limitation to the built-upof onshore wind turbines is analysed here by reducing their maximum installation capacityGmax,limn,onshore wind = owpGmaxn,onshore wind in each region n to a fraction owp of the geographicpotential Gmaxn,onshore wind defined previously.

The reduced onshore wind generation is almost completely replaced only by offshorewind, as shown in Fig. 5.1. The replacement is not linear with the reduction of onshorewind potential because some of the onshore installations can be moved to other regionswhich were not fully using their potentials previously and have only slightly worse windconditions. Even though offshore wind turbines have assumed capital costs twice as highas those on land, their average capacity factor is usually much higher and therefore theaverage energy generation cost are only slightly higher offshore than onshore. This can

71


0.0 0.2 0.4 0.6 0.8 1.0 1.2onshore wind potential

0

20

40

60

80

100

120Average system cost [€/MWh]

LV 0


LV 125


LV Opt


gassolar

onshore windoffshore wind

transmission linesPHS

run-of-riverreservoir hydro

Figure 5.1: Average total system costs per unit of generated energy in AC/MWh as function ofthe fraction owp of the onshore wind potential limit for the transmission line volumes of the zero,compromise, and optimal (left to right panels) grid. The total costs are divided into costs forthe modelled components battery storage (grey), H2 storage (magenta), gas (red), solar (yellow),onshore wind (blue), offshore wind (cyan), and transmission lines (black), top to bottom.

be seen in the only small increase of total system cost as the amount of onshore windinstallation potential is decreased down to zero. The costs change by less than 2.6% if thepotential is reduced by half and only up to 8.8%-12.2% if no onshore wind is allowed, withthe largest increase if transmission is also strongly limited.

Only for strongly reduced potentials are there some relatively small changes in otherparts of the system. Not all countries have access to the sea to build offshore turbines orhave sufficiently high capacity factors or installation potentials. If transmission capacitiesare restricted, they have to install slightly more solar and batteries, which increases costs.H2 storage can be reduced by up to 41%, but some long term storage is still necessary andthe overall effect is almost negligible.

The same effects are visible at country scale as shown in Figs. 5.2 and 5.3. Onshorewind capacity is replaced by offshore wind in countries bordering the North and BalticSea, and significantly extended in Denmark, the Netherlands, and eventually also in GreatBritain. Germany already builds the maximum installable capacity in the base scenarioand therefore does not replace its onshore wind power. Ireland also does not replace itsonshore wind, but the very large transmission capacities that connect Great Britain butalso Denmark to their southern neighbours suggest that the energy can now be producedefficiently and without a large grid connection to Ireland in more central nodes of thenetwork. Most countries in the southern half of Europe retain or slightly increase theirsolar capacity. If no onshore wind is allowed, France installs 45 GW of solar power butno local battery or H2 storage, while most other countries expand their battery storagetogether with the solar capacity. This suggests that the solar fluctuations in France canbe balanced by the more continuous offshore wind generation locally or through importsfrom the well connected Great Britain.

5.2.2 CO2 emission constraint

Setting a limit to the total European CO2 emissions is motivated by the policy goal to seta greenhouse gas emission budget to keep global temperature from increasing beyond a

72


Line volume = 239 TWkmTransmission lines (= 10 GW)Annual cost (= 5.0e9 Euro/a)



run-of-riverreservoir hydroPHSbattery storagehydrogen storage

gassolaronshore windoffshore wind

Figure 5.2: Map of average annual system costs per country in the optimal transmission scenariofor three levels of onshore wind potential 0% (top left), 50% (top right), 100% (bottom, base case)of the base assumption in each country. The area of the circles is proportional to the total costs percountry. The colors represent the shares of the different technologies. The modelled internationaltransmission lines are shown as black lines with width proportional to their optimized net transfercapacity.

AT BA BE BG CH CZ DE DK EE ES FI FR GB GR HR HU IE IT LT LU LV NL NO PL PT RO RS SE SI SK

country

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Local system cost [EU

R]

1e10battery storagehydrogen storagegassolaronshore wind

offshore windPHSrun-of-riverreservoir hydro

Figure 5.3: Same data as in Fig. 5.2 but as a more quantitative bar plot with explicit valuesof the local system cost and its composition and without representation of the transmission lines.The three bars for each country show respectively the level of onshore wind potential 0% (left bar),50% (middle bar), 100% (right bar).

73


0.0 0.1 0.2 0.3 0.4 0.5 0.6CO2 emissions / (1990 level)

0

20

40

60

80

100

120Av

erag

e sy

stem

cos

t [€/

MW

h]LV 0


LV 125


LV Opt

battery storagehydrogen storagegas (marginal)

gassolar




Figure 5.4: Average total system costs per unit of generated energy as function of the CO2

emission limit defined as fraction of the emission level of the year 1990, i.e. 1.6 Gtonne-CO2, forthe zero, compromise, and optimal transmission grid (left to right panels). The base scenariosassume a CO2 emission level of 5%. Same color code as in Fig. 5.1, except for gas costs, which arenow explicitly split into investment costs (rot) and marginal costs (orange). For an CO2 emissionlevel above 30%, the cost-optimal line volume is below 125 TWkm and therefore the compromiseand optimal transmission cases are identical.

certain level. The base scenario assumes a maximum CO2 emission limit CAPCO2 = 5%in units of the emission level in the year 1990, i.e., 77.5 Mt-CO2-equivalent per year forthe electricity sector [104].

This limit is already relatively strict, but CO2 emission can be brought down to zeroby replacing the remaining conventional generation. The only conventional generator andsource of CO2 emissions in the model are open-cycle gas turbines (OCGT) that are highlyflexible and have relatively low investment costs for power capacity, but high marginalcosts for energy generation and are therefore well suited to cover peak residual demand ina few hours per year.

Fig. 5.4 shows that the total system costs are an almost linear function of the CO2

emission limit close to CAPCO2 = 5% with a rate of −0.94 and −0.86 AC/MWh per per-centage point of CAPCO2 for compromise and optimal transmission volume, respectively.Therefore, a system with zero emissions has average system costs of 72 (69) AC/MWh, a6.6% (6.4%) increase from the base scenario, with the compromise (optimal) grid.

The conventional generator costs increase linearly with increasing emission limit, whilesolar and total wind installations decrease linearly. This leads to a linear decrease of thetotal generation costs at relatively low rates of −0.22 and −0.24 AC/MWh/% for compro-mise and optimal transmission volume, respectively. This indicates that the OCGT energycan be relatively easily replaced by linearly increasing renewable capacities.

Substitution of the required flexibility and power capacity to cover the variability ofrenewable generation can be done by additional storage units. The sum of the installedpower capacity of OCGT, battery, and H2 storage is almost constant at 49 ± 3% of thepeak demand for the compromise grid. Similarly, for the optimal grid the total powerof OCGT, battery, H2 storage, and offshore wind is 52 ± 2% of peak demand, relativelyindependent of the emission level. Battery and H2 storage costs and installed capacitieschange also almost linearly, but grow slightly faster than linear with decreasing CAPCO2

74


for emission limits close to zero. This is due to losses caused by storage use that in turnrequire additional generation.

This effect is very pronounced in the zero transmission scenario where the costs of boththe renewable generators and the storage units grow exponentially for CAPCO2 < 5%. Inthis case, countries with low capacity factors have to built comparatively many generatorsand storage capacity to have sufficient energy and flexibility at their disposal.

Storage units are only build in the model for CAPCO2 < 30%, 20%, 15% for the casesof zero, compromise, and optimal transmission line volumes, respectively. Above that, theconventional generators can produce enough energy to cover all fluctuations of the residualload.

If the transmission volume extension is only limited by economic costs, it decreaseslinearly with larger contributions from the conventional generators at a rate of -0.18AC/MWh/% or -6.8 TWkm/%, because there is both less renewable generation in thesystem that has to be smoothed, and more dispatchable energy available that allows tocover more fluctuations locally. For CAPCO2 > 30%, the contributions from conventionalgeneration are so large that the optimal line volume is smaller than the 125 TWkm of thecompromise case, and this exogenous constraint is no longer binding. At the maximumshare of OCGT, the line volume is 76.5 TWkm or 2.4 times today’s transmission volume.

The share of OCGT only increases with the emission limit until a cost equilibrium withthe other components in the system is reached. Any additional gas power generationwould increase the total system cost. This point CAP ∗

CO2 where the emission limit is nolonger binding can be calculated as

m · CAP ∗CO2 + b = Crenew (CAPCO2 =∞) (5.1)

from the slope m and intercept b of the fit to the cost of the renewable generators Crenewand its values for large emission limits Crenew(CAPCO2 =∞). This results in CAP ∗

CO2 =43% and 53%, for zero and optimal transmission, corresponding to emissions of 0.67 and0.82 Gtonnes-CO2/year, respectively.

Open cycle gas turbines are assumed to be the only conventional technology in thesystem due to their very high flexibility. This assumption starts to break down onceconventional generation is no longer needed only for peak load coverage. Today, otherconventional technologies, e.g. modern coal power plants, can be more economically effi-cient if less flexibility and more continuous bulk generation is required. This would lead toa slight reduction of total costs in the extreme case of large CO2 emission limits. A morethorough analysis of this effect would require detailed modelling of ramping constraintsand costs and lies beyond the focus of this work.

CO2 emission constraint without storage

In the previous section it was shown that installing battery and H2 storage is cost-effectiveonly if the CO2 emission limit is very low. In this section the consequences of removingstorage altogether are examined, both to understand better the economic necessity ofstorage and to analyse the case where large-scale storage is (for whatever reason) notfeasible.

See Fig. 5.5 for the cost development as the CO2 constraint is restricted for the case ofmoderate transmission expansion. For CO2 emission reductions to levels above 20%, the

75


0.0 0.1 0.2 0.3 0.4 0.5 0.6CO2 emissions / (1990 level), no storage

0

20

40

60

80

100

120

Average system

cost [€/MWh]

LV 125 TWkmbattery storagehydrogen storagegas (marginal)gassolaronshore wind

offshore windtransmission linesPHSrun-of-riverreservoir hydro

Figure 5.5: Same as Fig. 5.4 for the compromise grid but without battery or H2 storage includedin the model. The total system costs for the case including both storage technologies is markedas black dashed line. For emission levels above 20%, the results are identical to Fig. 5.4. Theoptimization did not converge for zero emissions. The smallest computed level of 0.1% has a totalcost of 149.6 AC/MWh (above plotted range).

results are the same as with storage. Below 20% the costs rise much faster, being 13.1%higher at 76.3 AC/MWh for 5% CO2, 48.6% higher at 106.9 AC/MWh for 0.5% CO2 andinfeasible for 0% CO2. There is also a significant increase in offshore wind as emissionsare reduced.

The reasons for these differences is the difficulty of bridging times with low wind andsun when there is neither storage nor backup from gas generation. Countries must eitherexpand their wind and solar capacities to compensate for the low power availability orimport from other regions where availability is better during these times (but even this isrestricted by the moderate transmission capacity). The model substitutes offshore wind foronshore wind because of its more regular production characteristics, but as CO2 emissionsare reduced, even this is not enough. With restricted transmission, no CO2 and no storage,the model finally becomes unsolvable at zero CO2 emissions.

CO2 emission shadow price

It is important to note that the results above assume a CO2 emission price of 0 AC/(tonne-CO2/year). Higher prices would lead to smaller economically optimal OCGT shares andemission levels. Fig. 5.6 plots the shadow price µCO2 of the global CO2 emission constraint(see eq. (10) of [62]) against CAPCO2. Here, µCO2 can be interpreted as the CO2 pricethat would be required for the market to achieve a certain emission level under the givenassumptions.

A restriction to the CAPCO2 = 5% level of the base scenario is economically optimalif the emission price is set to roughly 180 AC/(tonne-CO2/year) for both compromise andoptimal grid. In these transmission scenarios, the effect of the emission price is similarand the change of µCO2 with CAPCO2 is close to linear or mildly exponential down to

76



0

50

100

150

200

250

300

350

400

shadow

price [EUR

/(tonne-CO2

/a)] line volume [TWkm]

0125optimal

Figure 5.6: Shadow price of the global CO2 emission constraint as function of the CO2 emissionlimit CAPCO2 for the zero, compromise, and optimal (blue, green, red lines) transmission scenario.For exactly zero emissions, the shadow price diverges to around 20000 AC/(tonne-CO2/year), twoorders of magnitude larger than the plotted range. The green and red lines are partly overlapped.

very small emission limits. This indicates that the benefit of dispatchable energy dependsmore on peaks in the residual demand than on congestions in the available grid.

Only if no emissions are allowed, the CO2 shadow price jumps to around 20000 AC/(tonne-CO2/year), two orders of magnitude larger than the previous values. This suggests thatthere is a small number of hours per year when the power capacity of OCGT is veryvaluable for system stability even if very little energy can be produced. In practice, loadshedding should be a more viable option for these rare events, but is not included in themodel.

The flexibility from the dispatchable generators is much more valuable if fluctuationscannot be smoothed by transmission. In this case, µCO2 growths at a similar rate withdecreasing CO2 limit as with transmission but is higher by 60 to 100AC/(tonne-CO2/year)down to CAPCO2 > 10%. For stricter emission limits, µCO2 increases significantly faster atan exponential rate. CAPCO2 = 5% can be obtained by an emission price of 319AC/(tonne-CO2/year), while CAPCO2 = 0.5% requires an unrealistically high µCO2 = 1280AC/(tonne-CO2/year). This indicates how expensive CO2 reduction is when grid capacity is limited.

5.2.3 Heterogeneity

In the previous chapter is has been shown that cooperation and transmission grid expan-sion is an important factor to minimize total system costs. However, energy autonomythrough local renewable generation is sometimes perceived to be an important advantageover the conventional system that often requires fuel imports from other world regions.In this section, European transmission is still taken into account, but the share of energyproduced in each country is varied, similar to the methodology presented by [73].

The energy autonomy kn of country n can be defined as the ratio between the (average)

77


0.0 0.2 0.4 0.6 0.8 1.0energy autonomy limit

0

20

40

60

80

100

120

Average system

cost [€/MWh]

LV Optbattery storagehydrogen storagegassolaronshore wind

offshore windtransmission linesPHSrun-of-riverreservoir hydro

Figure 5.7: Average total system costs per unit of generated energy as function of the minimumenergy autonomy of each country. At a value of 0 no restriction is applied, until at 1 the averageenergy generation in each country must equal the average local energy demand per year, while thetransmission grid can still be used. Only the optimal transmission grid scenario is shown. At thesmaller grid volumes, the deviations from the base case are negligible. Transmission restrictionsalready enforce a certain level of energy autonomy.

generation and consumption in that country:

kn =〈∑

s gn,s,t〉〈dn,t〉

(5.2)

If kn = 1, the country is full autonomous in the sense that it produces on average asmuch energy per year as it consumes. However, it can still use transmission capacities forimports and exports if necessary, as long as the annual net balance kn − 1 is zero. Forkn < 1 or kn > 1, the country is a net importer or exporter, respectively. To constrainthe heterogeneity between countries, the minimum share of energy that each country hasto produce on average can be limited by the parameter K ∈ [0, 1]:

K ≤ kn ≤ max(1

K, K) (5.3)

Here, K = 0 applies no limits and corresponds to the base scenario, while K = 1 forces allcountries to generate at least their average consumption. In order to cover losses duringstorage use, the total generation always has to be larger than the demand, and thereforethe upper bound of the heterogeneity has to have a minimum value larger than 1. Here,K = 1.3 was chosen to ensure the convergence of the optimization in all cases.

The average system cost are essentially unchanged by the heterogeneity limit, as shownin Fig. 5.7 for optimized line volumes. The costs increase by no more than 2.8% and onlyfor very strict limits close to K = 1. The increase is caused by larger solar and offshorewind shares, but it is also slightly compensated by smaller onshore wind and transmissioninstallations.

In the base scenario, most net exporters are located in northern Europe and have good

78


onshore wind resources that are often imported by countries with relatively large solarshares. Therefore, if the generation is distributed more homogeneously, the solar installa-tion increases and the optimal grid volume decreases.

An exogenous restriction of the transmission volume can already enforce a certain levelof homogeneity by limiting import options. In the compromise grid scenario all countriesgenerate more than half of their consumption, kn ≥ 0.51, and therefore the heterogeneitylimit has no measurable influence (< 0.9%) on the total system cost or its composition.However, the distribution of generators between countries changes in a similar way asdescribed above.

These results show that the cost optimization is very robust against policy require-ments for homogeneously distributed generation, while at the same time the effects of gridexpansion remain unchanged.

5.2.4 Brexit / network topology

The sensitivity of the results towards changes in the network topology are analysed here bythe example of removing all transmission lines between the British Isles and continentalEurope in the model before the optimization, namely the two links connecting GreatBritain to respectively France and the Netherlands. This scenario is inspired by possibleconsequences of Great Britain leaving the EU and therefore called ‘Brexit’. The links areimportant in the network topology as it is usually techno-economically efficient to extendthem to large volumes (see Fig. 5.8) and they connect a very good wind region to the grid,as shown previously [62].

As a consequence of removing the link, the local system costs in Great Britain go downby 1.4% due to a decrease of installed onshore wind and H2 storage capacities as shownin Fig. 5.9. The country was a strong net exporter with a share of 7% of the total netexported energy in the system and the reduction of wind installations implies that GreatBritain can no longer sell as much excess generation. The total system costs thereforeincrease by 1.3% (2.9%) to 68.4 (66.7) AC/MWh in the compromise (optimal) line volumecase.

However, the local marginal price (LMP) in Great Britain goes up by 5.2% from 85.4 to89.8 AC/MWh after the removal of the link, i.e., electricity would become more expensivethere (see Fig. 5.9. The link was also used for balancing, but now the wind fluctua-tions have to be covered by significantly increased dispatchable gas generation with highmarginal costs.

After the ‘Brexit’, Ireland is now also disconnected from the main grid and is stronglyaffected by the lack of wind power exports. The installation costs even increase due to amuch higher share of conventional generation and the LMP grows by 13.2% from 80.8 to91.4 AC/MWh.

The missing imports from Great Britain can be compensated by larger installations ofoffshore wind in France, the Netherlands, and Greece as well as onshore wind in Germanyand Norway. The LMPs also increase in Denmark, Norway, Sweden, and Spain becausethey cannot sell as much excess power from existing installations since fluctuations canno longer be balanced by British wind generation. Instead, other countries have to installmore overcapacities for extreme events, and can produce more energy in hours when theyhad to import previously. The prices in the other countries also decrease because theshare of expensive gas generation in the main grid is lower. It must be shifted to Great

79







PHSbattery storage

hydrogen storagegas

solaronshore wind

offshore wind

Figure 5.8: Map of average system costs per country for base scenario (left) and Brexit (right)for compromise (top) and optimal (bottom) line volumes. The figures in the left column showresults that were already discussed in [62]. The area of the circles is proportional to the total costsper country. The modelled international transmission lines are shown as black lines with widthproportional to their optimized net transfer capacity.

80


AT BA BE BG CH CZ DE DK EE ES FI FR GB GR HR HU IE IT LT LU LV NL NO PL PT RO RS SE SI SK

country

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Local system cost [EU

R]

1e10battery storagehydrogen storagegassolaronshore windoffshore windPHSrun-of-riverreservoir hydro

EU AT BA BE BG CH CZ DE DK EE ES FI FR GB GR HR HU IE IT LT LU LV NL NO PL PT RO RS SE SI SK

country

0

1

2

3

4

5

Energy gen

eration / d

eman

d

gassolaronshore windoffshore windrun-of-riverreservoir hydro

<EU> AT BA BE BG CH CZ DE DK EE ES FI FR GB GR HR HU IE IT LT LU LV NL NO PL PT RO RS SE SI SK

country

0

20

40

60

80

100

120

140

Loca

l mar

gina

l pric

e [E

UR/M

Wh] brexit

0 1

Figure 5.9: Local system costs (top panel), energy generation (middle), and locational marginalprice (bottom) per country before (left bars) and after (right bars) a ‘Brexit’ scenario, i.e., usageof the transmission links between Great Britain and respectively France and the Netherlands isprohibited. This does not affect the limit of the global transmission line volume. The compromisetransmission grid case with a line volume of 125 TWkm is shown.

81


0.0 0.2 0.4 0.6 0.8 1.0 1.2solar capital cost

020406080100120

Average system cost [€/MWh]

LV 0


LV 125


LV Opt


gassolar




Figure 5.10: Composition of the average total system costs per unit of generated energy asfunction of the fraction of the solar PV capital cost assumption for the zero, compromise, andoptimal (left to right panels) transmission grid scenarios.

Britain and Ireland to satisfy security-of-supply constraints, but the total amount of energyproduced by gas is still constant due to the global CO2 emission limit.

5.3 Sensitivity to cost assumptions

Estimates for the future development of costs for technologies that are expected to undergovery large-scale deployment for the first time are intrinsically uncertain. Especially solarPV and storage costs could potentially drop significantly over the next decades. Sincecost assumptions play an important part in energy system modelling, it is important toquantify the impact of deviations from the costs in the base scenario. The sensitivity to thecosts is tested here by varying the capital investment and fixed operation and maintenancecost assumptions for one technology at a time over a large range while keeping all othersat their base scenario value.

5.3.1 Solar capital costs

In the base scenario, investment costs for solar PV are assumed to be 600 AC/kW of installedcapacity. This value is already an extrapolation to the year 2030 and less than half of thecost in 2010, but could be reduced by another 30% until 2050 [60].

If the solar capital costs were indeed just 70% of the base value, or 420 AC/kW, theaverage total system costs would be reduced by 8% from 67.5 to 61 AC/MWh in thecompromise grid scenario, as shown in Fig. 5.10. The reduction of 6.5 AC/MWh is slightlylarger than the direct cost decrease of 4.4 AC/MWh that would occur if only the costs, butnot the installed capacity of solar PV are changed. This implies an effective additionalbenefit to the system due to the shift to a higher solar share from 61 TW to 83 TW of2.1 AC/MWh, or 3.1% of the total costs when reducing solar costs by 30%.

Even though the total system costs are relatively sensitive to solar cost assumptions,most changes are linear with moderate slopes down to 50%–70% of the solar cost. Withdecreasing solar costs, the installed capacity, generated energy, and curtailment of winddecrease. It is replaced by additional solar and battery and solar capacity. Additionally,the power capacity of H2 storage is almost completely replaced by OCGT capacity (see

82



0.00.51.01.52.02.53.03.54.04.5

Powe

r cap

acity

[TW] LV 0


LV 125


LV Opt


gassolar


PHSrun-of-river

reservoir hydro

Figure 5.11: Composition of the total installed power capacity of generators and storage unitsas function of the fraction of the solar PV capital cost assumption for the zero, compromise, andoptimal (left to right panels) transmission grid scenarios. The peak of the total demand of 517GW is marked as horizontal dashed black line.


0.00.20.40.60.81.01.21.4

Energy

gen

eration / d

eman

d

LV 0


LV 125


LV Opt

gas solar onshore wind offshore wind run-of-river reservoir hydro

Figure 5.12: Composition of the total generated energy in units of the total demand as functionof the fraction of the solar PV capital cost assumption for the zero, compromise, and optimal (leftto right panels) transmission grid scenarios. Energy generation above the demand is caused bylosses from storage use. The amount of curtailed energy is not shown.

Fig. 5.11. This indicates that balancing the demand locally becomes a slightly more domi-nant solution compared to spatial and long-term smoothing of wind generation, especiallyin countries with good solar resources. Therefore, the transmission volume in the optimalgrid scenario also decreases but stays above 125 TWkm, the volume of the compromisegrid.

In the extreme case that solar becomes very cheap compared to the other technologies,there is an upper limit of 70% of the consumed energy that can be provided by solar alone,as shown in Fig. 5.12. However, this requires huge solar power capacities of up to 2.9 TW,5.6 times the peak demand. At the same time, a significant amount of solar energy of upto 30% of the yearly consumption has to be curtailed, leading to an inefficient system withlow effective capacity factor. At 40% of the solar cost, solar provides 50% of the energy,with a power capacity of three times peak demand and little curtailment, and thereforecomparatively high efficiency.

Fig. 5.13 shows that the amount of curtailed energy remains relatively constant withdecreasing solar capital costs at around 8% to 12% of the demand until solar costs are

83



0.0

0.1

0.2

0.3

0.4

0.5Cu

rtailed energy / demand

LV 0


LV 125


LV Opt

solar onshore wind offshore wind run-of-river

Figure 5.13: Composition of the total curtailed energy in units of the total demand as functionof the fraction of the solar PV capital cost assumption for the zero, compromise, and optimal (leftto right panels) transmission grid scenarios. The order of curtailment is, if possible, offshore wind,onshore wind, solar.

roughly cut in half. Even lower costs would lead to the installation of significant overca-pacities of solar generation and therefore a strong increase in curtailed energy of up to40% of the demand.

This points towards practical and modelling limitations of solar shares that are largerthan what would be cost optimal for solar capital costs smaller than 50% of the baseassumption. The excess energy could potentially be utilized, e.g., by shifting some of thedemand or allowing additional demand via sector coupling to create additional revenue ifthat demand is flexible enough. These options are not considered in the model.

However, this could lead to additional stress on the grid if the consumption is not veryclose to the PV panels. Especially if a significant share of PV is decentral the low voltagedistribution grid might require a massive expansion or it could become unstable due tosuch large power fluctuations. This effect is not seen by the model.

With currently implemented control mechanisms that are designed for a centralizedsystem, even the large scale curtailment of excess solar generation might be difficult tocoordinate if there are large numbers of independently operated installation owned bymany different stakeholders.

5.3.2 Battery capital costs

Even though modern battery technology has been commercially available for severaldecades, their capital costs dropped significantly over the last few years due to tech-nological developments and scaling effects in the manufacturing process [22]. Budischaket al. [61] estimate a price drop by roughly 70% between 2008 and the 2030 values of310 AC/kW for power and 145 AC/kWh for energy capacity used in the base scenario.

However, the modelling results presented here are quite robust against even large changesof battery costs down to 25% of the base assumption, as shown in Fig. 5.14. Even in thatcase, the total system costs decrease by only 10.6% (7%) to 61 AC/MWh (60.6 AC/MWh)in the compromise (optimal) grid scenario. Without interconnecting transmission, storagehas to provide a large amount of flexibility to ensure system stability. Therefore the totalsystem costs are more sensitive to the storage cost and decrease by 14.3% to 73.6 AC/MWhfor the same battery cost change.

84


0.0 0.5 1.0 1.5 2.0battery capital cost

020406080100120


LV 0


LV 125


LV Opt


gassolar




Figure 5.14: Composition of the average total system costs per unit of generated energy asfunction of the fraction of the battery capital cost assumption for the zero, compromise, andoptimal (left to right panels) transmission grid scenarios.


0.00.51.01.52.02.53.03.54.04.5

Powe

r cap

acity

[TW

] LV 0


LV 125


LV Opt


gassolar


PHSrun-of-river

reservoir hydro

Figure 5.15: Composition of the total installed power capacity of generators and storage unitsas function of the fraction of the battery capital cost assumption for the zero, compromise, andoptimal (left to right panels) transmission grid scenarios. The peak of the total demand of 517GW is marked as horizontal dashed black line.

The installed battery power increase exponentially with decreasing cost from 0.12 TWto 0.41 TW at 25% of the costs (see Fig. 5.15). However, the solar share increases onlylinearly at a low rate as more battery capacity becomes available, but stays below 35%of the generated energy. The batteries allow more short-term smoothing and thereforemore efficient usage of fluctuating solar generation. This also reduces the required windcapacities, and replaces to a larger extend the more capital intensive offshore wind power.Additionally, the long-term H2 storage can be completely removed due to a lower windshare and higher solar energy efficiency. The peak demand coverage it provided in a fewhours per year can then be replaced by additional OCGT power capacity.

For very small capital costs, the increase of power capacity P of the batteries as functionof the cost factor fc becomes even faster and turns into a power law P ∝ fmc with powerm = −0.76 to −0.86, depending on transmission scenario, i.e., it rises faster than indirectlyproportional to the costs. This is due to the interaction with onshore wind power. Thebattery energy capacity is now large enough for long-term storage and can smooth evenwind fluctuations over at least several days. Onshore wind is the cheapest renewablegenerator type in the model in terms of investment cost per average producible energy

85


0.0 0.5 1.0 1.5 2.0H2 storage capital cost

020406080100120


LV 0


LV 125


LV Opt


gassolar




Figure 5.16: Composition of the average total system costs per unit of generated energy asfunction of the fraction of the H2 storage capital cost assumption for the zero, compromise, andoptimal (left to right panels) transmission grid scenarios.

and can therefore reduce the system costs by replacing solar and offshore wind installationsif power balancing is not an issue.

5.3.3 Hydrogen storage capital costs

Hydrogen (H2) storage that is charged by electrolysis of water and discharged via a fuelcell is not yet in use as large scale energy storage application. Its cost and efficiencyparameters are characterized by relatively expensive power capacity, but cheap energycapacity with low round-trip efficiency when compared to battery storage. This makes itadequate for a long-term, large energy storage profile with relatively low usage frequency.As a commercial large scale implementation is not yet available, large deviations from thebase assumption are possible and tested here.

The modelling results are even more robust against changes of the H2 storage costs thanof the battery costs as shown in Fig. 5.16. The total system costs are virtually the sameas in the previous section down to 25% of the base cost assumptions, after which they fallslightly slower with decreasing H2 storage costs.

However, the composition of the system now remains almost constant even for a 75%cost reduction that leads to a capacity increase by a factor of 4.3 (see Fig. 5.17). Theshare of onshore wind increases only slightly as the H2 storage cost is decreased. However,onshore wind was already the dominant energy source in the system, but can still bemade more effective by additional long-term storage. Simultaneously, some of the solarinstallations and eventually all battery capacities are removed. Even though the round-tripefficiency of batteries is significantly higher, inexpensive and large H2 storage capacities,in combination with the increased wind installations, provide enough flexibility to thesystem to even compensate most short-term solar fluctuations.

The installed power capacity of the conventional gas turbines (OCGT) quickly decreasesto almost zero already at 80% H2 costs, but never vanishes and the amount of generatedenergy remains the same and is only limited by the CO2 emission constraint. The OCGTpower capacity decreases because there is sufficiently large H2 storage capacity whichallows to cover all demand peaks mostly from wind energy that previously had to becurtailed but can now be stored in large quantities and over sufficiently long periods.In turn OCGT power does not have to be preserved for extreme hours, but is used by

86



0.00.51.01.52.02.53.03.54.04.5

Powe

r cap

acity

[TW

] LV 0


LV 125


LV Opt


gassolar


PHSrun-of-river

reservoir hydro

Figure 5.17: Composition of the total installed power capacity of generators and storage units asfunction of the fraction of the H2 storage capital cost assumption for the zero, compromise, andoptimal (left to right panels) transmission grid scenarios. The peak of the total demand of 517GW is marked as horizontal dashed black line.

the model as a relatively cheap energy source that is operated almost continuously overthe whole year and only shuts down during peak solar production. This maximizes thecapacity factor of OCGT and avoids most of its capital costs.

If H2 storage is more expensive than in the base assumption, the previously discussedtrends reverse, H2 storage is relatively quickly replaced by OCGT, battery, and solarcapacity and is no longer used if the costs are increased to more than 175% for both thecompromise and the optimum grid scenario. Without transmission, storage is much moreimportant for the system stability and 36% of the H2 storage capacity is still built even ifits cost doubles.

5.3.4 Onshore wind capital cost

Wind turbines are a relatively mature technology and have already been deployed ona large scale in recent years, even though there is still significant additional installationpotential in Europe. Especially offshore wind turbines are also expected to undergo furthertechnological development that will lead to cost reductions. Ref. [60] assumes a decreaseto respectively 1075 and 2093 AC/kW by 2050 for onshore wind and offshore wind, a 9.1%and 16.5% reduction from the 2030 costs.

The optimization results are relatively sensitive even to these small changes of the windcost assumptions. Fig. 5.18 shows for the compromise grid that after a 25% reduction ofthe onshore wind cost, the total system costs decrease by 10.4% while the onshore windpower increases by 72.9%. Half of the offshore wind and a third of the solar installationsare no longer required. This higher share of onshore wind generators also leads to a 51.5%increase of the curtailed energy to 10.9% of the demand. Should the onshore wind costunexpectedly decrease even further, these trends would continue until no offshore wind isbuilt at 50% and almost no solar at 25% of the cost. Replacing these last solar capacitiesis possible with a very large onshore wind power capacity, but would lead to a very largeamount of curtailed energy of up to 1.3 times the annual demand. If, however, the onshorewind cost should increase by 25%, up to 42.2% of its installations would be replaced byoffshore and solar capacity.

87


0.0 0.2 0.4 0.6 0.8 1.0 1.2onshore wind capital cost

020406080

100120

Aver

age

syst

em c

ost [

€/M

Wh]

LV 125


gassolar





0.00.51.01.52.02.53.03.54.04.5

Powe

r cap

acity

[TW

] LV 125


0.0

0.1

0.2

0.3

0.4

0.5

Curta

iled

ener

gy /

dem

and LV 125

Figure 5.18: Left : Composition of the average total system costs per unit of generated energyas function of the fraction of the onshore wind capital cost assumption. All panels are for thecompromise transmission grid scenario. Middle: Composition of the total installed power capacityof generators and storage units as function of the fraction of the solar PV capital cost assumption.The peak of the total demand is marked as horizontal dashed black line. Right : Composition ofthe total curtailed energy in units of the total demand as function of the fraction of the solar PVcapital cost assumption. The curtailment at zero cost is 1.3 times the total demand.

0.0 0.2 0.4 0.6 0.8 1.0 1.2offshore wind capital cost

020406080

100120

Aver

age

syst

em c

ost [

€/M

Wh]

LV 125


gassolar





0.00.51.01.52.02.53.03.54.04.5

Powe

r cap

acity

[TW

] LV 125


0.0

0.1

0.2

0.3

0.4

0.5

Curta

iled

ener

gy /

dem

and LV 125

Figure 5.19: Same as Fig. 5.18 but as function of the fraction of the offshore wind capital costassumption. The curtailment at zero cost is 0.57 times the total demand.

5.3.5 Offshore wind capital cost

The total system costs are less sensitive to changes of the offshore wind cost, but stilldecrease by 7.4% with a 25% lower offshore wind cost assumption with the compromisegrid, as shown in Fig. 5.19. Reducing offshore wind costs leads to an linear increase of itspower capacity. It replaces mostly onshore wind while the solar capacity remains relativelystable and is only slight decreased. This leads to a significant decrease of the total powercapacity by up to 21.3% compared to the base case at a large range of 50% to at least10% of the assumed cost. At the same time, the amount of curtailed energy remains at oreven below the initial value until the offshore wind cost assumptions are halved.

In the limit of very small offshore wind costs, the share of onshore wind is negligible, butsolar can still contribute to a cost-optimal system with 241 GW or 14.8% of the total powercapacity. This suggest a positive correlation due to a different spatial distribution and thedifferent generation profile of solar that helps to mitigate line congestions during hours of

88

5.4 Sensitivity to changes of physical input parameters

0.0 0.2 0.4 0.6 0.8 1.0 1.2on&offshore wind capital cost

020406080

100120

Average system

cost [€/MWh]

LV 125


gassolar





0.00.51.01.52.02.53.03.54.04.5

Powe

r capacity [T

W] LV 125


0.0

0.1

0.2

0.3

0.4

0.5

Curta

iled energy / demand LV 125

Figure 5.20: Same as Fig. 5.18 but as function of the fraction of both the onshore wind and theoffshore wind capital cost assumption. The curtailment at zero cost is 2.6 times the total demand.

high demand if large amounts of power have to be transported from remote offshore windinstallations.

5.3.6 Onshore and offshore wind capital cost

Fig. 5.20 shows that the system costs decreases even faster than in the previous cases ifboth the onshore and offshore wind cost assumptions are reduced simultaneously. As inthe offshore wind case, the total installed power capacity decreases as the offshore windinstallations are expanded and can provide more energy to the system, but a significantamount of solar power is now replaced by an increasing share of onshore wind. For verysmall cost assumptions, the results are similar to the onshore wind case with additionaloffshore wind installations that require even larger amounts of curtailed energy.


The exact amount of capacity required to ensure system stability often depends on onlya few hours per year when the combination of low generation potential, possibly depletedstorage systems, and congested lines has to meet a high demand. It is important toconsider a representative period of weather data to take into account a sufficiently largenumber of these random fluctuations and rarely occurring extreme events. This also helpsto avoid over-optimization of the generator fleet to a single year of input data.

5.4.1 Different single weather years

First, the single year optimizations of the base scenario (2011) are repeated for the weatherand load data of the years 2012 to 2014. Fig. 5.21 shows that the optimal system con-figuration depends to some extend on the simulated year and the total costs range from62.6 to 67.9 AC/MWh for the compromise grid volume. The relative changes of both totalcost and composition of the system are similar in all transmission cases. The standarddeviation of the total cost over the four years is respectively 3.5%, 3.8%, and 2.7% of themean value, for zero, compromise, and optimal grid volume.

The differences in total system cost are correlated with changes of the peak and totalannual electricity consumption, as plotted in Fig. 5.22. The system costs decrease system-

89


2011 2012 2013 2014data year

020406080

100120

Average system

cost [EU

R/MWh]

LV 0

2011 2012 2013 2014data year

LV 125

2011 2012 2013 2014data year

LV Opt


gassolar




Figure 5.21: Composition of the average total system costs per unit of generated energy forthe four different weather and demand input years 2011 to 2014 (left to right bars) for the zero,compromise, and optimal (left to right panels) transmission grid scenarios.

3.10 3.11 3.12 3.13 3.14 3.15Total demand [EWh/a]

180

200

220

240

260

280

Total system cost [billio

n €]

LV0 125 TWkm Opt

505510515520525530535540Peak demand [GW]

180

200

220

240

260

280

Total system cost [billio

n €]

3.10 3.11 3.12 3.13 3.14 3.15Total demand [EWh/a]

500505510515520525530535540545

Peak dem

and [GW]

data year2011 2012 2013 2014

Figure 5.22: Correlations between total system costs, total demand, and peak demand in thedata years 2011 to 2014 (circle, triangle, star, square markers) for the zero, compromise, optimal(blue, green, red lines) grid volume. The dashed lines are only intended as a visual guide.

atically with reductions of total and peak demand, except for the data year 2012. In thisyear, the ratio of peak to total demand is much larger than in the other years, and thesystem cost is slightly higher than expected from the total consumption. However, it isstill much lower than a linear extrapolation from the peak load values would indicate. Thissuggests that the amount of installed power capacity and therefore total cost is mostlydetermined by the amount of energy the system has to provide, which already impliessignificant over-installation of capacity compared to the peak demand, while coverage ofthe peak demand only requires additional installations in relatively extreme cases.

The average capacity factor cf of the renewables is defined here as

cf =

∑n 〈gn,s,t〉t ·G

maxn,s∑

nGmaxn,s

(5.4)

It is the average amount of energy 〈gn,s,t〉t that can be produced per unit of installedcapacity, weighted by the respective installation potential Gmaxn,s in country n, and plotted

90


2011 2012 2013 2014data year

0.97

0.98

0.99

1.00

1.01

averag

e ca

pacit

y factor (n

ormed

) onshore windoffshore windsolar

Figure 5.23: Average capacity factor cf of onshore wind (blue), offshore wind (cyan), and solar(yellow) for different weather years, normalized to the cf = 0.233, 0.485, 0.128 for offshore wind,onshore wind, and solar of the data year 2011. The data points are marked by circles, the dashedlines are only visual aids.

in Fig. 5.23. For an easier comparability of the relative changes, the values in the figurehave been normalized to the cf = 0.485, 0.233, 0.128 for offshore wind, onshore wind, andsolar of the data year 2011.

The composition of the system in terms of shares of onshore wind and solar installationsis largely determined by the capacity factor. For the weather years with capacity factorlower than in 2011, the installed capacities are also proportionately lower, and vice versa.The size of offshore wind installations does not follow the same trend but remains relativelystable. This could be related to the fact that offshore wind is only built in a few countries,or that the average capacity factor is much higher and therefore the benefit of relativelysmooth generation is more important than a slightly lower capacity factor.

The regional distribution of the generators is shown in Fig. 5.24 and follows the expectedtrends. In the data year 2013 where the solar capacity factor is lowest, the countries thatare usual solar dominated such as Spain and Italy have to install significant shares ofonshore wind, while in 2014, when the total solar share is relatively high, there are solarinstallations as far north as Poland. The transmission capacity have to be redistributedonly to a small extend to adapt to the slightly different generator layouts.

A lack of correlation of the total system cost with the potential renewable generationis indicated by the higher system cost in the data year 2012 despite the higher onshorewind and only marginally lower offshore wind capacity factor when compared to 2011.This suggests that the limited installation potentials of the renewables do not restrict thesystem configuration strongly, and therefore that a significantly higher consumption, e.g.,through the electrification of other sectors, could be covered.

These first indications should be set on a more solid statistical ground once a largernumber of data years becomes available. The analysis could also be refined by studyingthe influence of persisting extreme events where relatively high demand and low generationpotential appear continuously over long periods of time. They might be a better indicator

91


Year: 2011Transmission lines (= 10 GW)Annual cost (= 5.0e9 Euro/a)





PHSbattery storage

hydrogen storagegas

solaronshore wind

offshore wind

Figure 5.24: Map of average annual system costs per country in the optimal transmission scenariofor the four individual years of weather and demand data 2011 to 2014 (left to right, top to bottom).The area of the circles is proportional to the total costs per country. The modelled internationaltransmission lines are shown as black lines with width proportional to their optimized net transfercapacity.

92


1 2 3 4optimization period [years]

020406080100120


LV 0


LV 125


LV Opt


gassolar




Figure 5.25: Composition of the average system cost per unit of generated energy for differentnumbers of simulated weather and consumption years starting from 2011 for the zero, compro-mise, and optimal (left to right panels) transmission grid scenarios. The color code indicates thecontributions of different technologies.

for increased system cost than the peak demand, but this is beyond the scope of this work.

5.4.2 Multi-year optimization

Instead of modelling the system for a single year of weather and load data, it can alsobe optimized for a longer period of continuous input data. This results in a solutionthat might be more stable and realistic because it is adapted to a potentially larger spec-trum of generation and demand situations. Starting from the weather and load year 2011considered in the base scenario, 1 to 4 years of continuous data are simultaneously opti-mized here. Fig. 5.25 shows that with the compromise grid the average total system costs67.1 ± 0.7 AC/MWh deviate very little from the value 67.5 AC/MWh of the base scenario.It is also close to the maximum cost of the single year simulations (2012: 67.8 AC/MWh),indicating that the system capacity is set by a few extreme events over the whole period.The maximum cost difference between the four year and the single year simulations is3.5 AC/MWh, a 5.5% increase from the value of the weather year 2014. This is a lowerbound for the uncertainty a single year optimization has compared to long-term modelling.

The lack of change of the total system costs compared to the single year optimizationsdespite the decrease of average annual consumption from 2011 to 2014 demonstrates thatthe year 2012 with the highest individual cost also determines most of the required capacityfor the whole period under consideration. This can likely only be mitigated by inexpensivemeans to store energy over a long period of time or by appropriate demand managementduring the events that define the capacity requirements.

Similar to the single year optimizations, the shares of onshore wind and solar instal-lations in the multi-year models are proportional to the corresponding average capacityfactors. However, the changes in both quantities are significantly smaller, as indicated inFig. 5.26.

The variations of the total system costs are similarly small in all transmission casessuch that the standard deviation between the different numbers of simulated years isnever larger than 0.8% of the mean. This indicates that the transmission volume has noadditional impacts on the results other than those discussed before. The same effect can

93


1.0 1.5 2.0 2.5 3.0 3.5 4.0optimization period [years]

0.97

0.98

0.99

1.00

1.01

average capacity factor (normed)

onshore windoffshore windsolar

Figure 5.26: Same as Fig. 5.23, but for capacity factor cf averaged over different numbers ofyears starting from 2011.

also be seen for the single year optimizations.

5.4.3 3h sampling

Some weather data sets, e.g. [105], provide data only in a lower temporal frequencyof 3h. Computational restrictions might also prevent optimization at a higher frequency,especially if a very long time period should be considered. At a lower frequency, the numberof optimization variables and therefore the memory requirements are proportionately lowerand also the computational solving time might decrease by a similar magnitude. Both canbe limiting factors.

The time resolution was decreased by taking 3-hour means of the hourly values of thedemand and potential renewable generation time series. The system was then optimizedboth for the data year 2011 and the three-year period 2011 to 2013. Fig. 5.27 shows thatthe share of solar power increases and replaced wind if the sampling frequency is lower Thisis due to the much stronger fluctuations of solar generation an hourly timescale comparedto wind. The temporal averaging implicitly simulates the smoothing effects of a short termstorage and increases the effective capacity factor. This effect is not as pronounced in thewind timeseries as their dominant fluctuations occur on larger timescales. The batterycapacity also decreases with the time resolution as

This indicates that models with time resolution less frequent than one hour might tendto overestimate the effectiveness of solar generation and therefore underestimate batteryand wind generation requirements. However, in the scenario discussed here, the overalleffects are small and are even outweighed by the fluctuations due to modelling a differentperiod of weather and demand data.

94

5.5 Summary and conclusions

hydro ror

PHS

links

offwind

onwind

solar

OCGT H2

batte

ry

0

5

10

15

20

25

30Av

erage system

costs [€

/MWh]

LV 0Nyears,freq(1, 1h)(1, 3h)(3, 1h)(3, 3h)

hydro ror

PHS

links

offwind

onwind

solar

OCGT H2

batte

ry

LV 125 Nyears,freq(1, 1h)(1, 3h)(3, 1h)(3, 3h)

hydro ror

PHS

links

offwind

onwind

solar

OCGT H2

batte

ry

LV Opt Nyears,freq(1, 1h)(1, 3h)(3, 1h)(3, 3h)

Figure 5.27: Average system cost of all modelled technologies over total consumption for all fourcombinations of 1 and 3 simulated years starting from 2011 at 1-hour and 3-hour time resolution(left to right bars) for the zero, compromise, and optimal (left to right panels) transmission gridscenarios. The time resolution was decreased by taking 3-hour means of the hourly values of thedemand and potential renewable generation time series.

5.5 Summary and conclusions

In the previous chapter, a highly renewable European electricity system has been modelledand optimized for minimal total system cost while guaranteeing security of supply. Thevolume of inter-connecting transmission lines has been varied over a large range from theeconomically optimal size to zero with non-linearly increasing total system costs, and acompromise level of four times today’s transmission was found that reduces the costs bynearly a third compared to zero transmission.

This chapter analyses for these three levels of transmission the sensitivity of the resultsof this model to variations of several key assumptions that are uncertain due to possiblechanges of policy decision, economic and technological developments, or physical inputparameters.

Most of the restrictions due to policy considerations only lead to relatively small changesof the minimal system costs. If the maximum installable capacity of onshore wind tur-bines are restricted, they can be replaced by offshore wind installations at comparablecost. The allowed CO2 emission level can be relatively easily adjusted and brought to zeroas long as moderate amounts of storage and transmission are available. Without theseoptions, very strict CO2 limits are expensive to achieve. The other considered restrictions,stricter requirements for self-sustainability of individual countries and changes of the net-work topology, have an even smaller impact on the total system cost but influence thedistribution of local assets. The small changes in total system cost indicate that policy re-quirements can be accommodated to a large extend without significant cost penalties. Thisallows policy makers to choose compromise solutions relatively independent of economicconsiderations.

The robustness against changes of the cost assumptions of battery or H2 storage showsthat they provide a certain, but limited benefit to the system due to their flexibilitythat can smooth fluctuations of renewable generation. This is not strongly dependent onstorage costs. Either of the two technologies can be easily replaced individually with some

95


modifications to the system configuration but without very strong increase of total cost.However, a complete removal of both storage technologies increases the costs significantly,unless the CO2 emission constraint is relaxed and more dispatchable energy becomesavailable. If, in contrast, the CO2 level should also be decreased, the system very quicklybecomes much more expensive and the costs diverge for zero dispatchable energy.

The results are sensitive to changes of generator cost assumptions. However, the effectremains at or below the order of 10% of the total system cost for the expected additionalcost decreases [60] of respectively roughly 10%, 17%, and 30% for onshore wind, offshorewind, and solar between the base year 2030 for the cost assumption to 2050. This is stillsmaller than the cost changes due to restriction of the transmission grid.

Similar to the results discussed in the previous chapter, there are consistent correlationsbetween the amount of installed onshore wind power, transmission lines, and long termstorage, as well as between solar power and batteries that are due to smoothing effectsof the fluctuating generation. In addition to that, a positive interaction between offshorewind and solar power is revealed if the offshore wind capacity is increased significantly,which is due to the different feed-in characteristics that allow peak demand coverage bysolar and batteries, and a different spatial distribution that helps to avoid grid congestions.

The results are qualitatively similar if other input data years are modelled, with smallchanges in total cost and optimal system composition. The total costs seem mostly deter-mined by annual energy consumption and to a lesser extend by peak demand but not somuch by the availability of renewables; if a given system has to cover demand over a longerperiod of several years, the system costs are determined by the requirement to be able tocover the most extreme demand situation even though it might only occur a few timesover a relatively short fraction of the considered period. The detailed composition of thesystem is more correlated with the relative share of average availability of the renewablegeneration.

Most of the above results that describe realistic variations of the system are at or belowthe level of cost changes due to strong restrictions of the transmission line volume, whichindicates that grid expansion is one of the most cost-effective methods in the design of alow-cost highly renewable European electricity network.

96

6 Conclusions

6.1 Main results

In this work the flexibility requirements of a highly renewable European electricity networkthat has to cover fluctuations of wind and solar power generation on different temporaland spatial scales are studied. Cost optimal ways to do so are analysed that includeoptimal distribution of the infrastructure, large scale transmission, storage, and dispatch-able generators. In order to examine these issues, a model of increasing sophistication isbuilt, first considering different flexibility classes of conventional generation, then addingstorage, before finally considering transmission to see the effects of each.

One of the biggest issue in the integration of renewable energy sources into the energymix is the adaptation to the fluctuating power generation, and one of the most promisingways to circumvent this problem is a smart large-scale interconnectivity of Europeancountries, as on these scales the fluctuations can be smoothed, as will be shown in thiswork in detail. We will explicitly study the energy network flexibility, as this is an excellentexample for the application of complex network theory, and this field of theoretical physicsis very well suited for the enhancement of renewable energy network integration.

Chapter 2 introduces a simplified model of the European electricity system where onlywind, solar, and conventional ‘backup’ generation can be used to cover the demand in anetwork of 30 countries in order to analyse the flexibility requirements at different shares ofrenewable generation. The availability of renewable generation is based on hourly historicalweather data over several years and the demand on the corresponding historical load data.The transmission network topology is simplified by considering only the extreme cases ofno transmission between countries or an unrestricted European network.

Three natural time scales on which the renewable generation and the demand fluctuatecan be observed. On the diurnal time scale, there are day/night variations of the consump-tion due to human activity and of the solar PV generation due to solar irradiation. Thesynoptic weather time scale is set by the typical persistence of weather patterns in Europeof three to ten days, which defines the dominant wind fluctuations. This scale also appearsin the demand variations between weekdays and weekends. The seasonal time scale canbe seen in the higher solar generation in the summer than in winter and more wind gen-eration in the winter than in summer. The consumption shows a similar seasonal patternas wind generation, but with a smaller amplitude. Therefore, the backup generators aredivided into three flexibility classes based on the maximum slope of the demand over thesetypical time scales. The capacity and dispatch of these abstract generator classes is thenoptimized to minimize total system costs, while still covering the residual load in almostall hours.

The seasonal generators are the dominant source of energy and have the largest installedcapacity for very low shares of renewable generation when there is a high, continuous baseload. However, they are less suited for systems with a more fluctuating residual load andcan therefore only be used effectively for systems where renewables generate less than half

97

6 Conclusions

of the average consumed energy.The useful capacity of medium flexible, synoptic generators increases with increasing

share of renewables until it reaches a peak at about 50% renewable generation when thefluctuations in the residual load are dominated by the variations of wind generation onthe synoptic weather time scale. For higher renewable shares, the typical fluctuations ofthe residual load occur on shorter and shorter time scales, and the synoptic generatorsbecome less effective.

The highly flexible generators usually have the lowest capital cost but the highestmarginal cost and therefore provide only a small share of energy and capacity if therenewable penetration is low and the residual load is relatively smooth. However, withincreasing share of renewables, the required capacity of the highly flexible generators in-creases significantly to a large fraction of the average demand. If only Germany as anisolated country without international transmission is considered, the required capacityof highly flexible generators is close to the average demand at a renewable gross shareof 100% and it does not decrease even if this share is increased to 200%. This indicatesthat there remains a small number of hours per year when very little renewable generationis available and the residual load remains high. This also means that the total installedcapacity can not be decreased significantly below the demand peak.

The main difference to the scenario with very large European interconnecting trans-mission expansion is that in the latter case the average total installed backup capacitydecreases significantly for large renewable penetrations. This is due to much smallerrequirements for highly flexible capacities because demand peaks can be covered by gen-eration in another country. Continental scale interconnection also allows to smooth windgeneration which is typically correlated over smaller distances of 600 to 1000 km, and there-fore reduces the need for synoptic flexibility. This reduces the need for synoptic backupflexibility and allows slightly more constant generation in the slowly flexible systems.

To reduce the amount of curtailed renewable generation, and thus reduce the need forbackup generation from non-renewable sources, this simplified model of the Europeanelectricity system is extended to include storage as an additional source of flexibility inchapter 3. This requires considering economic costs to allow for a realistic weightingbetween the technologies. Therefore, the three flexibility classes are not represented bythree abstract generators but instead by five currently used conventional technologiesfor which economic cost assumptions are available in the literature. This slightly differentmodelling approach leads to qualitatively similar results as before even though the mediumflexible capacity can now replace fast flexible capacities to a larger extent and up to largerrenewable gross shares with the peak now at 60% to 70% instead of 50% as before.

Two types of storage technologies are considered in this model. Central batteries provideshort-term storage with high power and low energy capacity and therefore act similar tofast flexible generators by smoothing demand peaks over a few hours. Hydrogen storagecan store larger amounts of energy but with a smaller power capacity and more lossesand thus supports the medium flexible generators by smoothing fluctuations on a longertimescale. Both storage technologies have the largest effect when the renewable grossshares are between 70% and 90% when they can efficiently utilize the curtailed renewablegeneration to cover residual demand.

In chapter 4 a more detailed and sophisticated model is developed that includes the op-timization of limited international transmission and therefore enables spatial heterogene-ity in the system which could not be taken into account before. It is used to analyse the

98

6.1 Main results

techno-economically optimal combination and distribution of infrastructure in a Europeanelectricity system. This allows to consider more explicitly the benefits of spatial aggre-gation through constrained transmission and temporal smoothing with storage that wereindicated in the previous chapters. The model focuses on a highly renewable Europeanelectricity system where the total annual CO2 emissions are reduced by 95% compared to1990. This allows to study the long-term target of a strongly decarbonised energy system.

The model considers the same 30 node network discussed above and also uses hourlyhistorical electricity demand and weather-based renewable generation data. Instead ofexternally controlled renewable shares, the linear cost optimization explicitly takes intoaccount the installation of onshore wind, offshore wind, and solar PV generators. Highlyflexible open-cycle natural gas turbines are the only source of CO2 emission, based onthe previous results that such a system requires only very flexible and inexpensive backupcapacity. Batteries and H2 storage with electrolysis of water and fuel cells are modelled asexemplary, expandable short- and long-term storage options, respectively. In addition, thealready existing pumped hydro storage, reservoir, and run-of-river generators are consid-ered but their capacities can not be expanded. The model then uses a linear optimizationto find the minimal total system costs, composed of annualized capital investment cost andmarginal operation costs, that ensures security of supply and satisfies the CO2 constraint.Additionally, a global transmission line volume limit can be enforced to systematicallystudy the effects of different levels of transmission grid expansion.

In the economically optimal case, such a highly renewable European electricity systemcan have total system costs of 65 AC/MWh, comparable to today’s system cost of 52–61AC/MWh. Its composition is dominated by onshore wind installations that contribute 56%to the total cost, followed by solar PV and offshore wind. Only relatively small storagecapacities are cost optimal, while the interconnecting transmission volume is expanded toroughly nine times today’s grid volume. However, such a large transmission grid expansionis likely to cause public acceptance issues.

Restricting transmission requires more storage to deal with the variability. This drivesup the total system costs by up to a third. However, the cost change is non-linear with asteep slope at small transmission volumes, but is almost flat for relatively large volumes.This allows to choose a compromise grid with three to four times today’s transmission linevolume that already locks in most of the cost benefits. This is also the grid volume thatwould be cost optimal if only underground cables would be built instead of the cheaper,but more visible overhead lines.

In the cost optimal grid case, the large transmission line volume allows to smooth therelatively cheap onshore wind energy over spatial scales larger than its typical correlationlength scale. More local solutions require more temporal smoothing via storage. It is morecost efficient to smooth the diurnal fluctuations of the solar PV generation with batteries(that have an expensive energy capacity but a relatively cheap power capacity and a highround trip efficiency) than the synoptic onshore wind variations over several days with H2

storage (that has an inexpensive energy capacity but expensive power capacity and a lowefficiency). Therefore, the solar share increases with restricted transmission, but the costsalso increase.

These results show that there are correlations between the shares of different technolo-gies in a cost optimal system: onshore wind benefits from large scale transmission lineexpansion and medium to long-term H2 storage, because they can smooth out some ofthe variability of the typical spatial and temporal scales, respectively. In contrast, the

99

6 Conclusions

solar PV generation can best be smoothed with short term battery storage, but does notprofit as much from grid expansion because its dominant spatial variations between dayand night are on the order of the diameter of the earth, much larger than the continentEurope.

In chapter 5, this model is analysed in more detail by studying the sensitivity of theresults to a number of parameters that are difficult to predict accurately. This includeschanges in external policy constraints, economic cost assumptions, and the physical inputparameters. The four considered policy assumptions are (1) restrictions of the maximumamount of installable onshore wind turbines, which can easily be replaced by additionaloffshore generators at very comparable cost; (2) variations of the CO2 emission level,which can be decreased to zero at only slightly higher cost as long as there is sufficienttransmission capacity and some storage options in the system. If in contrast the emissionlevel is increased, storage becomes less important and is not needed if the allowed CO2

emission is above 20% to 30% of the 1990 level; (3) requirements for energy autonomy (onaverage) in each country, which can be satisfied at virtually the same cost by redistributionof the infrastructure installed in the base scenario; and finally (4) a change of the networktopology inspired by a potential ‘Brexit’ scenario, which removes the export opportunitiesof the good wind resources in Great Britain and Ireland and increases the electricity pricethere and to a lesser extentin the rest of the system, but these net exports can be replacedby more offshore and onshore wind installations along the North Sea at comparable cost.

The considered variations of the policy assumptions have only a relatively little impacton the total system costs, which is smaller than the effect of restricting the expansion ofinterconnecting transmission. However, the composition of technologies and their spatialdistribution might change. This allows policy makers to base their energy system de-sign decisions on additional criteria without influencing the economic costs, even thoughdifferent decision makers might prefer slightly different options. It also shows that gridexpansion is an effective tool to reduce system costs in a highly renewable European elec-tricity system.

The results are sensitive to the cost assumptions of the solar PV, onshore and offshorewind generators if they deviate strongly from the base values. However, for the predictedcost decreases of up to 30% until 2050, the total system costs decrease by only up to 10%.If only one of battery or H2 storage costs are changed by up to 100%, the overall effect issmall as one storage type can replace the other if the shares of generator technologies thatare typically correlated with the storage technology (solar with batteries, onshore windwith H2 storage and transmission) are adapted accordingly.

However, the availability of at least one type of storage is important to provide sufficientflexibility to the system. If neither batteries nor H2 storage are available on a large scale,the system costs can increase significantly, depending on the amount of remaining flexi-bility, e.g., from dispatchable power. This agrees with the results discussed in chapter 3,where the use of storage was also shown to be not economic if the share of conventionalenergy in the system is large. However, with increasing renewable penetration, H2 storagecan contribute as a source of flexibility on the synoptic timescale. In both models, thebenefit of H2 storage increases with decreasing transmission capacity but both technologiescan contribute to an economically optimal system if the share of renewables is high.

Taking different, or more than one, weather and demand data years between 2011 and2015 into account for the cost optimization was shown to have relatively little impact.The results indicate that the total costs of the system depend mainly on the level of

100

6.2 Outlook

consumption, while its composition is correlated with the relative availability of the energysources. The statistical significance of these findings can be improved by taking furtherdata years into account and by considering other climate models. The impact of climatechange on the optimal energy system composition will be analysed, e.g., in the master’sthesis of M. Schlott [106], and first results indicate that the fluctuation time scale and thecorrelation length of wind power decreases, making interconnecting transmission and longterm storage more important.

To conclude, in this work it was shown that slowly flexible base load generators canonly be used in energy systems with renewable shares of less than 50%, independent ofthe expansion of an interconnecting transmission network within Europe. Furthermore,for a system with a dominant fraction of renewable generation, highly flexible generatorsare essentially the only necessary class of backup generators. The total backup capac-ity can only be decreased significantly if interconnecting transmission is allowed, clearlyfavouring a European-wide energy network. These results are independent of the com-plexity level of the cost assumptions used for the models. The use of storage technologiesallows to reduce the required conventional backup capacity further. This highlights theimportance of including additional technologies into the energy system that provide flexi-bility to balance fluctuations caused by the renewable energy sources. These technologiescould for example be advanced energy storage systems, interconnecting transmission inthe electricity network, and hydro power plants. It was demonstrated that a cost optimalEuropean electricity system with almost 100% renewable generation can have total systemcosts comparable to today’s system cost. However, this requires a very large transmissiongrid expansion to ten times the line volume of the present-day system. Limiting trans-mission increases the system cost by up to a third, however, a compromise grid with fourtimes today’s line volume already locks in most of the cost benefits. Therefore, it is veryclear that by increasing the pan-European network connectivity, a cost efficient inclusionof renewable energies can be achieved, which is strongly needed to reach current climatechange prevention goals. It was also shown that a similarly cost efficient, highly renewableEuropean electricity system can be achieved that considers a wide range of additionalpolicy constraints and plausible changes of economic parameters.

6.2 Outlook

The work presented here focuses on the properties of a future European electricity systemand thereby provides a basis for further analysis of the whole European energy sector. Inorder to fully limit CO2 emissions, energy generation in the heat and transport sectorsalso has to be decarbonised. In an upcoming paper based on [82] we show that thisis possible in a cost efficient way. Long-term thermal energy storage and the batteriesof electric vehicles can provide a large amount of flexibility on the diurnal, synoptic,and seasonal timescales. This allows an even stronger reduction of total system costthan the expansion of the interconnecting transmission network alone. The combinationof spatial smoothing of transmission with the temporal smoothing capabilities of sectorcoupling allows systems with lower costs than the present-day system. This highlights theimportance and effectiveness of a cross-sectoral, international approach to decarbonise theenergy system.

Further improvements to the model that are currently investigated include the influence

101

6 Conclusions

of climate change on the optimal composition and operation of the system, a significantincrease in spatial resolution of the network by increasing the number of simulated nodesper country in order to capture intra-country transmission restrictions as well as to finda more realistic and accurate spatial distribution of generators and storage, and a moredetailed analysis of the underlying economic market model and its effects. In future studieslong-term investment pathways for the build-up of these renewable energy systems shouldbe investigated that consider existing installations and economic lifetimes of all units,allow upgrading, fuel change, or premature decommissioning of installations. This canhelp to avoid technological lock-ins and indicates required policies or market designs thatare required to reach the economically optimal highly renewable energy systems that arethe subject of this work.

102

Zusammenfassung

In dieser Arbeit wird der Flexibilitatsbedarf eines hochgradig erneuerbaren europaischenStromnetzwerks untersucht, das die Schwankungen in der Energieerzeugung durch Wind-kraftanlagen und Solarzellenparks auf verschiedenen zeitlichen und raumlichen Skalen aus-gleicht. Verschiedene Methoden, dieses Netzwerk zu implementieren, werden auf ihre Kos-tenaspekte hin analysiert, insbesondere mit einem Augenmerk auf die Optimierung derInfrastruktur des Energienetzwerks, der internationalen Vernetzung, verschiedener Spei-chermoglichkeiten und der Einbeziehung konventioneller Energiequellen. Dazu wird dasModell im Zuge dieser Analyse in seiner Komplexitat zunehmend erhoht, um den Effekt dereinzelnen Optimierungen im Detail untersuchen zu konnen: Zunachst werden verschiede-ne Klassen konventioneller Kraftwerke mit unterschiedlicher Flexibilitat untersucht, dannwerden Stromspeicher hinzugefugt und schließlich der Einfluss paneuropaischer Vernet-zung auf das Energienetzwerk.

Die Arbeit beginnt mit einer Einleitung in das Feld der erneuerbaren Energiequellen,deren Abhangigkeit von Wetterbedingungen und den daraus resultierenden Problemati-ken ihrer Einbindung in das bestehende Energienetzwerk. Dieses erste Kapitel dient derEinbettung der vorliegenden Arbeit in das bereits bestehende Forschungsgebiet und derMotivation der Problematiken, die in dieser Forschungsarbeit untersucht werden.

Gegenstand des Kapitels 2 ist die Einfuhrung eines vereinfachten Modells des euro-paischen Stromnetzwerks, das ausschließlich Wind- und Solarenergie sowie konventio-nelle Energieerzeuger berucksichtigt, um den Energieverbrauch in einem Netzwerk be-stehend aus 30 europaischen Landern abzudecken. Mit diesem Modell wird der Flexibi-litatsbedarf bei unterschiedlichen Anteilen erneuerbarer Energiequellen getestet. Die Mo-dellierung der Verfugbarkeit der Energieerzeugung durch erneuerbare Energiequellen ba-siert auf stundlichen historischen Wetterdaten, die uber einen Zeitraum von mehrerenJahren hinweg dokumentiert wurden. Analog wird der Energiebedarf aus dokumentier-ten Verbrauchsdaten aus demselben Zeitraum errechnet. Da zunachst nur die Flexibilitatdes konventionellen Energieerzeugungssystems unter Einbindung hochfluktuierender er-neuerbarer Energiequellen untersucht werden soll, wird die Topologie des Netzwerks nichtexplizit berucksichtigt, sondern nur in den Moden unbeschrankte europaische Ubertragungbzw. keine europaische Vernetzung (d.h. einzelne Lander ohne Ubertragungsnetz) unter-sucht.

Aus den historischen Daten sind drei naturliche Zeitskalen erkennbar, auf denen sowohldie erneuerbare Energieerzeugung als auch der Energiebedarf fluktuieren: Auf einer tag-lichen Zeitskala treten Tag/Nacht-Fluktuationen auf, die auf der Verbraucherseite durchdie menschlichen Lebensgewohnheiten und auf der Erzeugungsseite durch die Sonnen-scheindauer erzeugt werden, d.h. Menschen schlafen nachts wenn auch die Sonne nichtscheint, wodurch sowohl der Energiebedarf als auch die Energieerzeugung verringert sind.Die synoptische Zeitskala wiederum wird durch die typische Lebensdauer der europaischenGroßwetterlagen dominiert, die sich ublicherweise alle drei bis zehn Tage verandern. DieseZeitskala ist die dominante Zeitskala, auf der die Erzeugung von Energie durch Windge-

103

Zusammenfassung

neratoren fluktuiert. Eine weitere synoptische Veranderungsgroße tritt auch als Muster imEnergieverbrauch auf, verursacht durch den unterschiedlichen Energiebedarf an Wochen-enden im Vergleich zu Werktagen. Schließlich ist noch eine saisonale Zeitskala erkennbar,da die langere und intensivere Sonnenscheindauer im Sommer zu einem hoheren Beitragaus Solarenergie fuhrt als im Winter, wahrend die Winderzeugung im Winter deutlicherhoht ist gegenuber den Sommermonaten, ebenso wie der Energiebedarf, der typischer-weise im Winter großer als im Sommer ausfallt. Daher werden die Backupkraftwerke in dreiFlexibilitatsklassen unterteilt, die auf der maximalen Anderungsrate des Verbrauchs aufdiesen drei typischen Zeitskalen basieren. Die Kapazitat und Energieerzeugung dieser ab-strakten Kraftwerksklassen werden optimiert, um die Gesamtsystemkosten zu minimieren,wahrend gleichzeitig die Residuallast (d.h. der Bedarf abzuglich der durch die erneuerbarenEnergiequellen erzeugte Leistung) gedeckt wird.

Aus diesem Modell lassen sich folgende Erkenntnisse direkt gewinnen: Solange der Anteilerneuerbarer Energien gering ist und es daher eine hohe Grundlast gibt, sind die saisonalenKraftwerke die dominante Energiequelle mit der großten installierten Kapazitat. Sie sindjedoch weniger gut geeignet sobald die Residuallast starker schwankt und konnen dahernur effizient eingesetzt werden solange der Energiebeitrag aus erneuerbaren Energiequellenanteilig unter 50% liegt.

Mit steigendem Anteil erneuerbarer Energien steigt auch die nutzliche Kapazitat dermittelflexiblen, synoptischen Kraftwerke, deren Nutzlichkeitsmaximum bei einem Anteilvon 50% erneuerbarer Energie erreicht ist. Bei diesem Anteil werden die Fluktuationender Residuallast durch Schwankungen in der Windenergieerzeugung auf der synoptischenWetterzeitskala dominiert. Oberhalb eines Anteils von 50% an erneuerbarer Energie fluktu-iert die Residuallast auf immer kurzeren Zeitskalen, wodurch die synoptischen Kraftwerkeimmer weniger effizient werden.

Die hochflexiblen Kraftwerke haben typischerweise die geringsten Investitionskosten,aber die hochsten Erzeugungskosten, weshalb ihr Beitrag zur Energieerzeugung und Ka-pazitat gering ist, solange der Anteil erneuerbarer Energien am Energiemix gering, unddaher die Residuallast relativ konstant ist. Je großer jedoch der Anteil erneuerbarer Ener-gieerzeugung, desto großer ist auch der Bedarf an hochflexiblen Kraftwerken, so dass selbi-ge schließlich den großten Teil des Kapazitatsbedarfs abdecken. Wird nur Deutschland alsisoliertes Land ohne paneuropaische Ubertragungsleitungen betrachtet, so ist die Kapa-zitat der hochflexiblen Kraftwerke so hoch wie der durchschnittliche Verbrauch bei einemBruttoanteil der erneuerbaren Energieerzeugung von 100%, und sinkt auch selbst bei ei-nem Bruttoanteil von 200% erneuerbarer Energien nicht. Dies ist dadurch bedingt, dass esimmer einige Stunden pro Jahr gibt, in denen kein Strom aus erneuerbaren Energiequellenerzeugt werden kann, und die hochflexiblen Kraftwerke also zur Notfallabdeckung dieserZeiten unabdingbar sind. Dies bedeutet weiterhin, dass die durch die hochflexiblen Kraft-werke bereitgestellte Kapazitat immer so hoch wie der maximale Verbrauch sein muss,um die Notfallabdeckung flachendeckend zu gewahrleisten, wenngleich diese dauerhafteBereitstellung hochst ineffizient ist.

Im Falle einer umfassenden paneuropaischen Vernetzung des Stromnetzes hingegen kanndie benotigte installierte Backupleistung stark reduziert werden bei einem hohen Anteilerneuerbarer Energie: Da viele der Verbrauchsspitzen durch Energieerzeugung in anderenLandern abgedeckt werden konnen, verringert sich der Bedarf an hochflexiblen Kraftwer-ken. Außerdem wird der Bedarf an synoptischen Kraftwerken dadurch reduziert, dass dieWindverhaltnisse sich innerhalb Europas auf Distanzen von etwa 600–1000km stark andern

104

Zusammenfassung

und somit immer irgendwo Windenergie generiert werden kann, selbst wenn in anderenRegionen Flaute herrscht. In diesem vereinfachten Modell konnen daher die saisonalenKraftwerke effizienter eingesetzt werden.

Alternativ zu einem erhohten Einsatz an Backupkraftwerken kann auch die Speicher-kapazitat im Netzwerk erhoht werden. Daher wird das Modell in Kapitel 3 um Speicherals eine weitere Flexibilitatsoption erweitert. Um eine faire Gewichtung zwischen den mo-dellierten Technologien zu gewahrleisten, werden außerdem konkrete okonomische Kos-tenannahmen benotigt. Dazu werden die drei abstrakten Flexibilitatsklassen nun durchfunf aktuelle konventionelle Technologien reprasentiert, fur die Kostenannahmen in derLiteratur verfugbar sind. Die aus diesen Kostenmodifikationen resultierenden Anderungensind relativ gering, der wesentliche Unterschied besteht darin, dass ein Teil der flexiblenKraftwerkskapazitat nun durch synoptische Kraftwerke abgedeckt werden kann, und sichdaher deren Nutzlichkeitsmaximum von vorher 50% auf nun 60–70% Anteil erneuerbarerEnergien verschiebt.

Zwei Arten von Speichertechnologien werden in diesem Modell berucksichtigt: Sta-tionare Batterien stellen Kurzzeitspeicherkapazitat mit hoher Leistungs-, aber geringerEnergiekapazitat zur Verfugung und verhalten sich daher ahnlich wie die hochflexiblenKraftwerke, indem sie Verbrauchsspitzen abfangen. Chemische Wasserstoffspeicher konnengroßere Energiemengen speichern als stationare Batterien, haben aber kleinere Leistungs-kapazitaten und hohere Verluste. Daher eignen sie sich vornehmlich zur Unterstutzungsynoptischer Kraftwerke, indem sie Fluktuationen auf langeren Zeitskalen kompensieren.Beide Speichertechnologien sind am effizientesten, wenn der Bruttoanteil erneuerbarerEnergieerzeugung zwischen 70–90% liegt, da in diesem Bereich der Energieuberschuss ameffizientesten genutzt werden kann.

Dieses Modell wird in Kapitel 4 noch einmal erweitert, dieses Mal um die gleichzeitigeOptimierung limitierter internationaler Ubertragungsleitungen, und berucksichtigt daherdie raumliche Heterogenitat im System, die bisher nicht betrachtet werden konnte. DasModell wird verwendet, um die techno-okonomisch optimale Zusammensetzung und Ver-teilung von Infrastruktur in einem europaischen Stromsystem zu analysieren. Dadurchkonnen die Vorteile der Transmission von Energie zwischen verschiedenen Gebieten, ins-besondere der daraus resultierende Ausgleich von Erzeugungsschwankungen zwischen denLandern, im Detail aufgezeigt werden. Dieses Modell betrachtet insbesondere ein Elek-trizitatssystem mit einem sehr hohen Anteil erneuerbarer Energien, in dem die gesamtejahrliche CO2 Emission um 95% gegenuber 1990 reduziert ist. Dies ermoglicht es, die Um-setzungsmoglichkeiten des Langzeitziels eines stark entkarbonisierten Energiesystems zustudieren.

Das Modell berucksichtigt dasselbe 30-Knoten-Netzwerk, das bereits zuvor verwendetwurde, und basiert auf stundlichen historischen Verbrauchsdaten und wetterbasierten Er-zeugungraten erneuerbarer Energiequellen. Die lineare Kostenoptimierung berucksichtigtexplizit die Installation von Onshore-Wind, Offshore-Wind und solaren PV-Generatorenanstelle eines vereinfachten, extern kontrollierten Anteils erneuerbarer Energien. Hochfle-xible Erdgasturbinen werden als einzige Quelle von CO2-Emissionen berucksichtigt aufGrund der vorhergegangen Erkenntnis, dass ein hochgradig erneuerbares Energiesystemausschließlich sehr flexible und kostengunstige Backupkapazitaten benotigt. Batterien undH2-Speicher mit Elektrolyse von Wasser und Brennstoffzellen werden als Beispiele fur aus-baubare Kurz- bzw. Langzeitspeicher modelliert. Des weiteren werden bereits existierendePumpspeicherkraftwerke, Stauwasserkraftwerke und Laufwasserkraftwerke berucksichtigt,

105

Zusammenfassung

allerdings kann deren Kapazitat nicht erweitert werden. Das Modell benutzt lineare Opti-mierung, um die minimalen Gesamtsystemkosten zu ermitteln, die sich aus jahrlichen Ka-pitalinvestmentkosten und Betriebskosten zusammensetzen, und dabei eine sichere Versor-gung und die Erfullung der CO2-Auflagen gewahrleisten. Zusatzlich kann eine Obergrenzedes Leitungsvolumens erzwungen werden, um den systematischen Effekt unterschiedlicherNetzausbaustufen zu untersuchen.

Im okonomisch besten Fall kann ein hochgradig erneuerbares europaisches Elektrizi-tatssystem Gesamtsystemkosten von 65 Eur/MWh erreichen, vergleichbar mit den heu-tigen Systemkosten von 52–61 Eur/MWh. Die Zusammensetzung dieses Energiemixes istdurch Onshore-Windinstallationen dominiert, deren Anteil an den Gesamtkosten bei 56%liegt, gefolgt von solaren PV-Anlagen und Offshore-Wind. Ein kostenoptimiertes Systementhalt nur wenige Speicherkapazitaten, wahrend das Ubertragungsleitungsvolumen aufdas neunfache des heutigen Ausbaus anwachst. Allerdings sind bei einem derartig großenNetzausbau Probleme bei der offentlichen Akzeptanz zu erwarten.

Eine Einschrankung des Leitungsausbaus fuhrt jedoch zu einem hoheren Bedarf an Spei-chern, was die Gesamtsystemkosten um bis zu einem Drittel erhoht. Dieser Kostenanstiegist nicht-linear und hat einen starken Anstieg bei kleinen Leitungsvolumina, wahrend dieKosten bei großen Volumina nahezu konstant sind. Daher kann ein Kompromissnetzwerkmit drei- bis vierfacher Ausdehnung des heutigen Leitungsvolumen bereits den Großteilder Kostenvorteile umfassen. Dies entspricht dem kostenoptimalen Leitungsvolumen, daserreicht werden konnte unter der Voraussetzung, dass alle Leitungen unterirdisch (unddamit kostenintensiv) verlegt werden.

Im kostenoptimierten Falle erlaubt das große Leitungsvolumen die vergleichsweise guns-tigen Onshore-Windenergien großflachig zu verteilen, wahrend begrenzte Netzwerkkonfi-gurationen einen starkeren zeitlichen Ausgleich durch Speicher erfordern. Es ist deutlichkosteneffizienter, die taglichen Schwankungen der solaren PV Erzeugung mit Batterienzu kompensieren, als die synoptischen Onshore-Windschwankungen uber einen Zeitraumvon mehreren Tagen mit H2-Speichern auszugleichen. Daher steigt der Anteil solarer er-neuerbarer Energie mit Beschrankung des Leitungsvolumens, wahrend die Gesamtkostenparallel ansteigen.

Dieses Resultat zeigt, dass es starke Zusammenhange zwischen den Anteilen verschiede-ner Technologien in einem kostenoptimierten System gibt: Onshore-Windintegration wirdbegunstigt durch großflachigen Netzausbau und durch mittel- bis langfristige Speiche-rung in H2-Speichern, da diese die typischen raumlichen und zeitlichen Schwankungen derWinderzeugung ausgleichen. Die kurzzeitskalien Schwankungen der Solarenergie konnenhingegen mit Batteriespeichern kompensiert werden, wahrend ein Ausbau der Leitungennur zu einer geringen Verbesserung der Nutzbarkeit der Solarenergie fuhrt, da die domi-nante raumliche Variation der Solarenergie die Großenordnung des Erddurchmessers hat,die deutlich großer ist als der Kontinent Europa.

In Kapitel 5 wird dieses Modell noch detaillierter analysiert, indem die Sensitivitatder Ergebnisse bezuglich verschiedener Parameter untersucht wird, die nicht oder nurschwer korrekt vorhergesagt werden konnen. So konnen sich beispielsweise die politi-schen Rahmenbedingungen, okonomische Kostenentwicklungen, aber auch die Wetterda-ten mittel- bis langfristig stark andern. Die vier folgenden politischen Annahmen werdenvariiert und auf ihre Konsequenzen hin analysiert: (1) Beschrankungen der Maximalan-zahl installierbarer Onshore-Windturbinen. Diese konnen jedoch relativ leicht durch wei-tere Offshoregeneratoren ersetzt werden, bei vergleichbaren Kosten. (2) Variationen des

106

Zusammenfassung

CO2-Emissionslevels. Dieses kann bis auf null herabgesenkt werden bei vergleichsweise ge-ringer Kostenerhohung, solange ausreichende Leitungskapazitat und Speichermoglichkeitgewahrleistet ist. Wird jedoch das zulassige Emissionslevel erhoht, verringert sich dieBedeutung der Speicherkapazitat, bis sie schließlich bei einem CO2-Emissionswert von20%–30% des Wertes von 1990 bedeutungslos wird. (3) Das Bedurfnis zur Energieun-abhangigkeit der einzelnen Staaten kann leicht erfullt werden zu vergleichbaren Kostendurch Anpassung der installierten Infrastruktur. (4) Eine Veranderung der Netzwerktopo-logie durch den Brexit, bei dem die Exportmoglichkeiten guter Windresourcen aus Groß-britannien und Irland entfernt werden, was zu einer Erhohung des Strompreises vor allemin Großbritanninen, aber zu einem geringeren Teil auch im Rest Europas, fuhrt. Die-se Nettoexporte konnen allerdings innerhalb Resteuropas durch einen hoheren Anteil anOffshore- und Onshore-Windinstallationen entlang der Nordseekuste zu vergleichbarenKosten kompensiert werden.

Die berucksichtigten Variationen der Parameter auf Grund politischer Einschrankungenhaben nur einen geringen Einfluss auf die Gesamtsystemkosten, und ihr Einfluss ist deut-lich geringer als der der Beschrankung des Leitungsnetzausbaus. Es andern sich nurdie Zusammensetzung und die raumliche Verteilung der Technologien. Dies ermoglichtes den Entscheidungstragern beim Design des Energiesystems zusatzliche Kriterien zuberucksichtigen, um beispielsweise die offentliche Akzeptanz zu steigern, ohne gleichzei-tig die Gesamtkosten zu verandern. Hiermit wird klar gezeigt, dass ein Ausbau des Lei-tungsnetzes ein sehr effektive Methode zu Verringerung der Kosten in einem hochgradigerneuerbaren europaischen Elektrizitatsnetz ist.

Die Ergebnisse sind sensitiv zu den Kostenannahmen fur Solar-, Onshore- und Offshore-Generatoren sofern sie stark von den Grundannahmen abweichen. Fur die vorhergesagteKostenabnahme von 30% bis 2050 senken sich die totalen Systemkosten allerdings nur ummaximal 10%. Falls sich die Kosten fur nur einen der beiden Speichertypen (Batterien undH2-Speicher) um 100% andern, fallt der Effekt dennoch klein aus. Prinzipiell kann ein Spei-chertyp durch den anderen ersetzt werden, sofern die zugehorige Stromerzeugungstechno-logie entsprechend variiert wird. Allerdings muss mindestens eine Speichertechnologie imSystem vorhanden sein, um die notwendige Flexibilitat zu gewahrleisten. Falls keine Formvon Speichern großskalig im Netzwerk vorhanden ist, konnen die Systemkosten signifikantansteigen, in Abhangigkeit der verbleibenden Flexibilitat, zum Beispiel durch steuerbareKraftwerke. Dies bestatigt noch einmal das Ergebnis aus Kapitel 3 in dem bereits gezeigtwurde, dass Speicher erst dann okonomisch sind, wenn der Anteil konventioneller Energieim System niedrig ist.

Eine Erweiterung der Ausgangsdatenlagen im Bezug auf historische Wetter- und Ver-brauchsdaten um den Zeitraum zwischen 2011 und 2015 hatte nur einen relativ geringenEinfluss auf die Kostenoptimierung des Systems. Dieses Resultat zeigt, dass die Gesamt-systemkosten hauptsachlich vom Verbrauch abhangen und nicht von der Verfugbarkeitder erneuerbaren Energiequellen, wahrend die Zusammensetzung des Energiemixes vonder Verfugbarkeit der Energiequellen abhangt. Die statistische Signifikanz der Resultatekann durch die Berucksichtigung weitere Datenjahre und Klimamodelle verbessert werden.So wird zum Beispiel der Einfluss des Klimawandels auf die optimierte Systemzusammen-setzung in der Masterarbeit von M. Schlott [106] analysiert, und erste Resultate deutenbereits darauf hin, dass die Fluktuationszeitskala und die Korrelationslange von Wind-kraft abnimmt, was internationalen Leitungsausbau und Langzeitspeicherintegration umso wichtiger macht.

107

Zusammenfassung

Zusammenfassend wurde in dieser Arbeit klar gezeigt, dass der Ausbau des Energie-netzwerkes innerhalb Europas unabdingbar ist, um die Klimaziele von Paris zu erreichen.Desweiteren wurde gezeigt, dass das Erreichen dieses Ausbaus mit den vorhandenen er-neuerbaren Energiequellen moglich ist und einer flachendeckenden Energieversorgung ba-sierend auf erneuerbaren Energien weniger die Gesamtsystemkosten als vielmehr politischeund sozio-okonomische Randbedingen im Wege stehen.

108

Bibliography

[1] S. Levitus, J. I. Antonov, T. P. Boyer, O. K. Baranova, H. E. Garcia, R. A. Locarnini,A. V. Mishonov, J. R. Reagan, D. Seidov, E. S. Yarosh, M. M. Zweng, World oceanheat content and thermosteric sea level change (0–2000 m), 1955–2010, GeophysicalResearch Letters 39 (10) (2012) n/a–n/a. doi:10.1029/2012GL051106.

[2] J. Oerlemans, Extracting a climate signal from 169 glacier records, Science308 (5722) (2005) 675–677. doi:10.1126/science.1107046.

[3] E. Rignot, S. Jacobs, J. Mouginot, B. Scheuchl, Ice-shelf melting around Antarctica,Science 341 (6143) (2013) 266–270. doi:10.1126/science.1235798.

[4] UNFCCC, Adoption of the paris agreement, Tech. rep., UNFCCC, re-port No. FCCC/CP/2015/L.9/Rev.1, http://unfccc.int/resource/docs/2015/cop21/eng/l09r01.pdf (2015).

[5] W. F. Ruddiman, Earth’s Climate: Past and Future, 2nd Edition, W. H. Freeman,2008.

[6] P. Tans, R. Keeling, Trends in atmospheric carbon dioxide, http://www.esrl.noaa.gov/gmd/ccgg/trends/, accessed July 2017 (2017).

[7] S. F. Green, M. H. Jones, An Introduction to the Sun and Stars, Cambridge - OpenUniversity, 2015.

[8] A. Khazendar, E. Rignot, E. Larour, Acceleration and spatial rheology of Larsen CIce Shelf, Antarctic Peninsula, Geophysical Research Letters 38 (9) (2011) n/a–n/a,l09502. doi:10.1029/2011GL046775.

[9] J. E. Walsh, F. Fetterer, J. Scott Stewart, W. L. Chapman, A database for depictingarctic sea ice variations back to 1850, Geographical Review 107 (1) (2017) 89–107.doi:10.1111/j.1931-0846.2016.12195.x.

[10] B. Kroposki, B. Johnson, Y. Zhang, V. Gevorgian, P. Denholm, B. M. Hodge,B. Hannegan, Achieving a 100% renewable grid: Operating electric power systemswith extremely high levels of variable renewable energy, IEEE Power and EnergyMagazine 15 (2) (2017) 61–73. doi:10.1109/MPE.2016.2637122.

[11] L. Jiang, C. Wang, Y. Huang, Z. Pei, S. Xin, W. Wang, S. Ma, T. Brown, Growthin wind and sun: Integrating variable generation in China, IEEE Power and EnergyMagazine 13 (6) (2015) 40–49. doi:10.1109/MPE.2015.2458754.

[12] T. Ma, Network studies of the Chinese electricity grid, Bachelor thesis, FrankfurtInstitute for Advances Studies (FIAS) (2016).

109

http://dx.doi.org/10.1029/2012GL051106

http://dx.doi.org/10.1126/science.1107046

http://dx.doi.org/10.1126/science.1235798

http://unfccc.int/resource/docs/2015/cop21/eng/l09r01.pdf

http://unfccc.int/resource/docs/2015/cop21/eng/l09r01.pdf

http://www.esrl.noaa.gov/gmd/ccgg/trends/

http://www.esrl.noaa.gov/gmd/ccgg/trends/

http://dx.doi.org/10.1029/2011GL046775

http://dx.doi.org/10.1111/j.1931-0846.2016.12195.x

http://dx.doi.org/10.1109/MPE.2016.2637122

http://dx.doi.org/10.1109/MPE.2015.2458754

Bibliography

[13] B. A. Frew, S. Becker, M. J. Dvorak, G. B. Andresen, M. Z. Jacobson, Flexibilitymechanisms and pathways to a highly renewable US electricity future, Energy 101(2016) 65–78. doi:10.1016/j.energy.2016.01.079.

[14] O. Edenhofer, R. Pichs-Madruga, Y. Sokona, K. Seyboth, S. Kadner, T. Zwickel,P. Eickemeier, G. Hansen, S. Schlomer, C. von Stechow (Eds.), Renewable energysources and climate change mitigation: Special report of the intergovernmental panelon climate change, Cambridge University Press, 2011.

[15] International Energy Agency, Key world energy statistics 2017, Tech. rep., In-ternational Energy Agency, Paris, France, https://www.iea.org/publications/freepublications/publication/KeyWorld2017.pdf (2017).

[16] Jacobson, M.Z., Delucchi, M.A., Providing all global energy with wind, water, andsolar power, Part I: Technologies, energy resources, quantities and areas of infras-tructure, and materials, Energy Policy 39 (3) (2011) 1154–1169.

[17] Rossby et al., Relation between variations in the intensity of the zonal circulationof the atmosphere and the displacements of the semi-permanent centers of action,J. Marine Res. 2 (1939) 38–55.

[18] J.-F. Mercure, P. Salas, An assessement of global energy resource economic poten-tials, Energy 46 (1) (2012) 322–336. doi:10.1016/j.energy.2012.08.018.

[19] IRENA, IRENA Ocean Energy Technology Brief 3: Tidal energy technology, Tech.rep., International Renewable Energy Agency (IRENA), http://www.irena.org/DocumentDownloads/Publications/Tidal_Energy_V4_WEB.pdf, online, accessedSeptember 2017 (2014).

[20] Eurostat, Eurostat energy database, http://ec.europa.eu/eurostat/, tablenrg 105a, accessed July 2017 (2017).

[21] F. Cherubini, N. D. Bird, A. Cowie, G. Jungmeier, B. Schlamadinger, S. Woess-Gallasch, Energy- and greenhouse gas-based LCA of biofuel and bioenergy systems:Key issues, ranges and recommendations, Resources, Conservation and Recycling53 (8) (2009) 434–447. doi:10.1016/j.resconrec.2009.03.013.

[22] B. Nykvist, M. Nilsson, Rapidly falling costs of battery packs for electric vehicles,Nature Climate Change 5 (4) (2015) 329–332. doi:10.1038/nclimate2564.

[23] F. Meneguzzo, R. Ciriminna, L. Albanese, M. Pagliaro, The great solar boom: aglobal perspective into the far reaching impact of an unexpected energy revolution,Energy Science & Engineering 3 (6) (2015) 499–509. doi:10.1002/ese3.98.

[24] IRENA, Battery storage for renewables: market status and technologyoutlook, Tech. rep., International Renewable Energy Agency (IRENA),http://www.irena.org/DocumentDownloads/Publications/IRENA_Battery_

Storage_report_2015.pdf, online, accessed September 2017 (2015).

[25] T. W. Brown, T. Bischof-Niemz, K. Blok, C. Breyer, H. Lund, B. V. Mathiesen,Response to ’Burden of proof: A comprehensive review of the feasibility of 100%renewable-electricity systems’, ArXiv e-prints, in Review. arXiv:1709.05716.

110

http://dx.doi.org/10.1016/j.energy.2016.01.079

https://www.iea.org/publications/freepublications/publication/KeyWorld2017.pdf

https://www.iea.org/publications/freepublications/publication/KeyWorld2017.pdf


http://www.irena.org/DocumentDownloads/Publications/Tidal_Energy_V4_WEB.pdf

http://www.irena.org/DocumentDownloads/Publications/Tidal_Energy_V4_WEB.pdf

http://ec.europa.eu/eurostat/

http://dx.doi.org/10.1016/j.resconrec.2009.03.013

http://dx.doi.org/10.1038/nclimate2564

http://dx.doi.org/10.1002/ese3.98

http://www.irena.org/DocumentDownloads/Publications/IRENA_Battery_Storage_report_2015.pdf

http://www.irena.org/DocumentDownloads/Publications/IRENA_Battery_Storage_report_2015.pdf

http://arxiv.org/abs/1709.05716

Bibliography

[26] M. Gotz, J. Lefebvre, F. Mors, A. M. Koch, F. Graf, S. Bajohr, R. Reimert, T. Kolb,Renewable power-to-gas: A technological and economic review, Renewable Energy85 (Supplement C) (2016) 1371–1390. doi:10.1016/j.renene.2015.07.066.

[27] D. Schlachtberger, S. Becker, S. Schramm, M. Greiner, Backup flexibility classes inemerging large-scale renewable electricity systems, Energy Conversion and Manage-ment 125 (2016) 336–346, Sustainable development of energy, water and environmentsystems for future energy technologies and concepts. doi:10.1016/j.enconman.

2016.04.020.

[28] D. Heide, L. von Bremen, M. Greiner, C. Hoffmann, M. Speckmann, S. Bofinger,Seasonal optimal mix of wind and solar power in a future, highly renewable Europe,Renewable Energy 35 (11) (2010) 2483–2489. doi:10.1016/j.renene.2010.03.

012.

[29] EU member countries, National Renewable Energy Action Plans, http://ec.

europa.eu/energy/renewables/action_plan_en.htm, Online, accessed Feb 2016(2010).

[30] H. Holttinen, Hourly wind power variations in the nordic countries, Wind Energy8 (2) (2005) 173–195. doi:10.1002/we.144.

[31] IEA, Harnessing Variable Renewables – A Guide to the Balancing Challenge, Tech.rep., International Energy Agency, Paris (2011).

[32] J. Ma, V. Silva, R. Belhomme, D. S. Kirschen, L. F. Ochoa, Evaluating and planningflexibility in sustainable power systems, in: Power and Energy Society General Meet-ing (PES), 2013 IEEE, IEEE, 2013, pp. 1–11. doi:10.1109/PESMG.2013.6672221.

[33] L. E. Jones (Ed.), Renewable Energy Integration – Practical Management of Vari-ability, Uncertainty, and Flexibility in Power Grids, Academic Press, LondonWaltham San Diego, 2014.

[34] B. Tarroja, F. Mueller, J. D. Eichman, S. Samuelsen, Metrics for evaluating theimpacts of intermittent renewable generation on utility load-balancing, Energy 42 (1)(2012) 546–562. doi:10.1016/j.energy.2012.02.040.

[35] M. Huber, D. Dimkova, T. Hamacher, Integration of wind and solar power in Europe:Assessment of flexibility requirements, Energy 69 (0) (2014) 236–246. doi:10.1016/j.energy.2014.02.109.

[36] E. Lannoye, D. Flynn, M. O’Malley, Evaluation of power system flexibility, PowerSystems, IEEE Transactions on 27 (2) (2012) 922–931. doi:10.1109/PESGM.2012.6345375.

[37] A. Ulbig, G. Andersson, On operational flexibility in power systems, in: Power andEnergy Society General Meeting, 2012 IEEE, IEEE, 2012, pp. 1–8. doi:10.1109/

PESGM.2012.6344676.

[38] A. Ulbig, G. Andersson, Analyzing operational flexibility of electric power systems,International Journal of Electrical Power & Energy Systems 72 (2015) 155–164.doi:10.1016/j.ijepes.2015.02.028.

111

http://dx.doi.org/10.1016/j.renene.2015.07.066

http://dx.doi.org/10.1016/j.enconman.2016.04.020




http://ec.europa.eu/energy/renewables/action_plan_en.htm

http://ec.europa.eu/energy/renewables/action_plan_en.htm

http://dx.doi.org/10.1002/we.144

http://dx.doi.org/10.1109/PESMG.2013.6672221




http://dx.doi.org/10.1109/PESGM.2012.6345375




http://dx.doi.org/10.1016/j.ijepes.2015.02.028

Bibliography

[39] S. Weitemeyer, D. Kleinhans, T. Vogt, C. Agert, Integration of renewable energysources in future power systems: The role of storage, Renewable Energy 75 (2015)14–20. doi:10.1016/j.renene.2014.09.028.

[40] F. Steinke, P. Wolfrum, C. Hoffmann, Grid vs. storage in a 100% renewable Europe,Renewable Energy 50 (2013) 826–832. doi:10.1016/j.renene.2012.07.044.

[41] B. V. Mathiesen, H. Lund, D. Conolly, H. Wenzel, P. Østergaard, B. Moller,S. Nielsen, I. Ridjan, P. Karnøe, K. Sperling, F. Hvelplund, Smart energy systemsfor coherent 100% renewable energy and transport solutions, Applied Energy 145(2015) 139–154. doi:10.1016/j.apenergy.2015.01.075.

[42] S. Schiebahn, T. Grube, M. Robinius, V. Tietze, B. Kumar, D. Stolten, Power to gas:Technological overview, systems analysis and economic assessment for a case studyin Germany, International journal of hydrogen energy 40 (12) (2015) 4285–4294.doi:10.1016/j.ijhydene.2015.01.123.

[43] K. Schaber, F. Steinke, T. Hamacher, Transmission grid extensions for the integra-tion of variable renewable energies in Europe: Who benefits where?, Energy Policy43 (2012) 123–135. doi:10.1016/j.enpol.2011.12.040.

[44] H. Kondziella, T. Bruckner, Flexibility requirements of renewable energy based elec-tricity systems–a review of research results and methodologies, Renewable and Sus-tainable Energy Reviews 53 (2016) 10–22. doi:10.1016/j.rser.2015.07.199.

[45] P. A. Østergaard, Reviewing energyplan simulations and performance indicator ap-plications in energyplan simulations, Applied Energy 154 (2015) 921–933. doi:

10.1016/j.apenergy.2015.05.086.

[46] G. B. Andresen, M. G. Rasmussen, R. A. Rodrıguez, S. Becker, M. Greiner, Fun-damental properties of and transition to a fully renewable pan-European powersystem, in: 2nd European Energy Conference, Vol. 33, 2012, p. 04001. doi:

10.1051/epjconf/20123304001.

[47] T. V. Jensen, M. Greiner, Emergence of a phase transition for the required amountof storage in highly renewable electricity systems, The European Physical JournalSpecial Topics 223 (12) (2014) 2475–2481. doi:10.1140/epjst/e2014-02216-9.

[48] R. A. Rodriguez, Weather driven power transmission in a highly renewable Europeanelectricity network, Ph.D. thesis, Aarhus University (2014).

[49] S. Becker, R. A. Rodrıguez, G. B. Andresen, S. Schramm, M. Greiner, Transmissiongrid extensions during the build-up of a fully renewable pan-European electricitysupply, Energy 64 (2014) 404–418. arXiv:1307.1723, doi:10.1016/j.energy.

2013.10.010.

[50] D. Heide, M. Greiner, L. von Bremen, C. Hoffmann, Reduced storage and balancingneeds in a fully renewable European power system with excess wind and solar powergeneration, Renewable Energy 36 (9) (2011) 2515–2523. doi:10.1016/j.renene.

2011.02.009.

112



http://dx.doi.org/10.1016/j.apenergy.2015.01.075

http://dx.doi.org/10.1016/j.ijhydene.2015.01.123

http://dx.doi.org/10.1016/j.enpol.2011.12.040

http://dx.doi.org/10.1016/j.rser.2015.07.199



http://dx.doi.org/10.1051/epjconf/20123304001

http://dx.doi.org/10.1051/epjconf/20123304001

http://dx.doi.org/10.1140/epjst/e2014-02216-9






Bibliography

[51] M. G. Rasmussen, G. B. Andresen, M. Greiner, Storage and balancing synergies ina fully or highly renewable pan-European power system, Energy Policy 51 (2012)642–651. doi:10.1016/j.enpol.2012.09.009.

[52] European Transmission System Operators, Country-specific hourly load data,https://www.entsoe.eu/data/data-portal/consumption/ (2011).

[53] D. L. Oates, P. Jaramillo, Production cost and air emissions impacts of coal cyclingin power systems with large-scale wind penetration, Environmental Research Letters8 (2) (2013) 024022. doi:10.1088/1748-9326/8/2/024022.

[54] K. Van den Bergh, E. Delarue, Cycling of conventional power plants: technicallimits and actual costs, Energy Conversion and Management 97 (2015) 70–77. doi:10.1016/j.enconman.2015.03.026.

[55] M. Jansen, C. Richts, N. Gerhardt, T. Lenk, M.-L. Heddrich, Strommarkt-Flexibilisierung: Hemmnisse und Losungskonzepte, Tech. rep., Fraunhofer-Institutfur Windenergie und Energiesystemtechnik (IWES), Energy Brainpool GmbH& Co. KG, online available at http://www.energybrainpool.com/services/

studienverzeichnis.html, accessed Mar 2015 (Jan. 2015).

[56] G. Varympopiotis, A. Tolis, A. Rentizelas, Fuel switching in power-plants: Modellingand impact on the analysis of energy projects, Energy Conversion and Management77 (2014) 650–667. doi:10.1016/j.enconman.2013.10.032.

[57] J. Apt, The spectrum of power from wind turbines, Journal of Power Sources 169 (2)(2007) 369–374. doi:10.1016/j.jpowsour.2007.02.077.

[58] E. Fertig, J. Apt, P. Jaramillo, W. Katzenstein, The effect of long-distance intercon-nection on wind power variability, Environmental Research Letters 7 (2012) 034017.doi:10.1088/1748-9326/7/3/034017.

[59] Bundesnetzagentur, Kraftwerksliste, http://www.bundesnetzagentur.de/cln_

1432/DE/Sachgebiete/ElektrizitaetundGas/Unternehmen_Institutionen/

Versorgungssicherheit/Erzeugungskapazitaeten/Kraftwerksliste/

kraftwerksliste-node.html, online, accessed Oct 2014 (Oct. 2014).

[60] A. Schroder, F. Kunz, J. Meiss, R. Mendelevitch, C. von Hirschhausen, Current andprospective costs of electricity generation until 2050, Data Documentation, DIW 68,Deutsches Institut fur Wirtschaftsforschung (DIW), Berlin, http://hdl.handle.

net/10419/80348, accessed July 2016 (2013).

[61] C. Budischak, D. Sewell, H. Thomson, L. Mach, D. E. Veron, W. Kempton, Cost-minimized combinations of wind power, solar power and electrochemical storage,powering the grid up to 99.9% of the time, Journal of Power Sources 225 (2013)60–74. doi:10.1016/j.jpowsour.2012.09.054.

[62] D. Schlachtberger, T. Brown, S. Schramm, M. Greiner, The benefits of cooperationin a highly renewable European electricity network, Energy 134 (2017) 469–481.doi:10.1016/j.energy.2017.06.004.

113


https://www.entsoe.eu/data/data-portal/consumption/

http://dx.doi.org/10.1088/1748-9326/8/2/024022



http://www.energybrainpool.com/services/studienverzeichnis.html

http://www.energybrainpool.com/services/studienverzeichnis.html


http://dx.doi.org/10.1016/j.jpowsour.2007.02.077

http://dx.doi.org/10.1088/1748-9326/7/3/034017

http://www.bundesnetzagentur.de/cln_1432/DE/Sachgebiete/ElektrizitaetundGas/Unternehmen_Institutionen/Versorgungssicherheit/Erzeugungskapazitaeten/Kraftwerksliste/kraftwerksliste-node.html




http://hdl.handle.net/10419/80348

http://hdl.handle.net/10419/80348

http://dx.doi.org/10.1016/j.jpowsour.2012.09.054


Bibliography

[63] EC, Energy roadmap 2050 – COM(2011) 885/2 (2011).

[64] G. Czisch, Szenarien zur zukunftigen Stromversorgung, Ph.D. thesis, UniversitatKassel (2005).

[65] Y. Scholz, Renewable energy based electricity supply at low costs - Development ofthe REMix model and application for Europe, Ph.D. thesis, Universitat Stuttgart(2012). doi:10.18419/opus-2015.

[66] F. Wagner, Surplus from and storage of electricity generated by intermittent sources,The European Physical Journal Plus 131 (12) (2016) 445. doi:10.1140/epjp/

i2016-16445-3.

[67] K. Schaber, F. Steinke, P. Muhlich, T. Hamacher, Parametric study of variablerenewable energy integration in Europe: Advantages and costs of transmission gridextensions, Energy Policy 42 (2012) 498–508. doi:10.1016/j.enpol.2011.12.016.

[68] R. A. Rodrıguez, S. Becker, G. B. Andresen, D. Heide, M. Greiner, Transmissionneeds across a fully renewable European power system, Renewable Energy 63 (Sup-plement C) (2014) 467–476. doi:10.1016/j.renene.2013.10.005.

[69] S. Hagspiel, C. Jagemann, D. Lindenberger, T. Brown, S. Cherevatskiy, E. Troster,Cost-optimal power system extension under flow-based market coupling, Energy 66(2014) 654–666. doi:10.1016/j.energy.2014.01.025.

[70] T. Brown, P.-P. Schierhorn, E. Troster, T. Ackermann, Optimising the Europeantransmission system for 77% renewable electricity by 2030, IET Renewable PowerGeneration 10 (1) (2016) 3–9. doi:10.1049/iet-rpg.2015.0135.

[71] A. Battaglini, N. Komendantova, P. Brtnik, A. Patt, Perception of barriers forexpansion of electricity grids in the European Union, Energy Policy 47 (2012) 254–259. doi:10.1016/j.enpol.2012.04.065.

[72] R. A. Rodriguez, S. Becker, M. Greiner, Cost-optimal design of a simplified, highlyrenewable pan-European electricity system, Energy 83 (2015) 658–668. doi:10.

1016/j.energy.2015.02.066.

[73] E. H. Eriksen, L. J. Schwenk-Nebbe, B. Tranberg, T. Brown, M. Greiner, Optimalheterogeneity in a simplified highly renewable European electricity system, Energy133 (Supplement C) (2017) 913–928. doi:10.1016/j.energy.2017.05.170.

[74] C. Bussar, M. Moos, R. Alvarez, P. Wolf, T. Thien, H. Chen, Z. Cai, M. Leuthold,D. U. Sauer, A. Moser, Optimal allocation and capacity of energy storage systemsin a future European power system with 100% renewable energy generation, EnergyProcedia 46 (2014) 40–47, 8th International Renewable Energy Storage Conferenceand Exhibition (IRES 2013). doi:10.1016/j.egypro.2014.01.156.

[75] J. Egerer, C. Lorenz, C. Gerbaulet, European electricity grid infrastructure expan-sion in a 2050 context, in: 10th International Conference on the European EnergyMarket, IEEE, 2013, pp. 1–7. doi:10.1109/EEM.2013.6607408.

114

http://dx.doi.org/10.18419/opus-2015

http://dx.doi.org/10.1140/epjp/i2016-16445-3

http://dx.doi.org/10.1140/epjp/i2016-16445-3




http://dx.doi.org/10.1049/iet-rpg.2015.0135





http://dx.doi.org/10.1016/j.egypro.2014.01.156

http://dx.doi.org/10.1109/EEM.2013.6607408

Bibliography

[76] H. Lund, A. N. Andersen, P. A. Østergaard, B. V. Mathiesen, D. Connolly, Fromelectricity smart grids to smart energy systems – a market operation based approachand understanding, Energy 42 (1) (2012) 96–102, 8th World Energy System Confer-ence, WESC 2010. doi:10.1016/j.energy.2012.04.003.

[77] H.-M. Henning, A. Palzer, A comprehensive model for the German electricity andheat sector in a future energy system with a dominant contribution from renew-able energy technologies–Part I: Methodology, Renewable and Sustainable EnergyReviews 30 (2014) 1003–1018. doi:10.1016/j.rser.2013.09.012.

[78] N. Gerhardt, A. Scholz, F. Sandau, H. Hahn, Interaktion EE-Strom, Warmeund Verkehr, Tech. rep., Fraunhofer IWES, http://www.energiesystemtechnik.iwes.fraunhofer.de/de/projekte/suche/2015/interaktion_strom_waerme_

verkehr.html (2015).

[79] V. Quaschning, Sektorkopplung durch die Energiewende, Tech. rep., HTW Berlin(2016).

[80] J. Deane, A. Chiodi, M. Gargiulo, B. P. O. Gallachoir, Soft-linking of a powersystems model to an energy systems model, Energy 42 (1) (2012) 303–312, 8th WorldEnergy System Conference, {WESC} 2010. doi:10.1016/j.energy.2012.03.052.

[81] D. Connolly, H. Lund, B. Mathiesen, Smart Energy Europe: The technical andeconomic impact of one potential 100% renewable energy scenario for the EuropeanUnion, Renewable and Sustainable Energy Reviews 60 (2016) 1634–1653. doi:

10.1016/j.rser.2016.02.025.

[82] T. Brown, D. Schlachtberger, A. Kies, M. Greiner, Sector coupling in a simplifiedmodel of a highly renewable European energy system, in: Proceedings of 15th WindIntegration Workshop, 2016.

[83] T. Brown, J. Horsch, D. Schlachtberger, Pypsa: Python for power system analysis,Journal of Open Research Software, accepted. arXiv:1707.09913.URL https://pypsa.org

[84] D. Schlachtberger, T. Brown, S. Schramm, M. Greiner, Supplementary Data: TheBenefits of Cooperation in a Highly Renewable European Electricity Network (Jun.2017). doi:10.5281/zenodo.804338.

[85] F. C. Schweppe, M. C. Caramanis, R. D. Tabors, R. E. Bohn, Spot Pricing ofElectricity, Norwell, MA: Kluwer, 1988.

[86] D. R. Biggar, M. R. Hesamzadeh, The Economics of Electricity Markets, Wiley,2014.

[87] Deutsche Energie-Agentur, DENA-Netzstudie II, online at http://www.dena.de/

publikationen/energiesysteme (2010).

[88] European Network of Transmission System Operators for Electricity, Ten-Year Net-work Development Plan (TYNDP) 2016, Tech. rep., ENTSO-E (2016).

115



http://www.energiesystemtechnik.iwes.fraunhofer.de/de/projekte/suche/2015/interaktion_strom_waerme_verkehr.html






https://pypsa.org


https://pypsa.org

http://dx.doi.org/10.5281/zenodo.804338

http://www.dena.de/publikationen/energiesysteme

http://www.dena.de/publikationen/energiesysteme

Bibliography

[89] J. Horsch, T. Brown, The role of spatial scale in joint optimisations of generationand transmission for European highly renewable scenarios, ArXiv e-printsarXiv:1705.07617.

[90] Gurobi Optimization, Inc., Gurobi optimizer reference manual, http://www.

gurobi.com (2016).

[91] G. B. Andresen, A. A. Søndergaard, M. Greiner, Validation of Danish wind timeseries from a new global renewable energy atlas for energy system analysis, Energy93, Part 1 (2015) 1074–1088. doi:10.1016/j.energy.2015.09.071.

[92] EEA, Corine land cover 2006 (2014).

[93] EEA, Natura 2000 data - the European network of protected sites, http://www.

eea.europa.eu/data-and-maps/data/natura-7 (2016).

[94] A. Kies, K. Chattopadhyay, L. von Bremen, E. Lorenz, D. Heinemann, RESTORE2050 Work Package Report D12: Simulation of renewable feed-in for power systemstudies., Tech. rep., RESTORE 2050, in preparation (2016).

[95] B. Pfluger, F. Sensfuß, G. Schubert, J. Leisentritt, Tangible ways towards climateprotection in the European Union (EU Long-term scenarios 2050), Fraunhofer ISI.

[96] European Transmission System Operators, Installed Capacity per Production Typein 2015, Tech. rep., ENTSO-E (2016).

[97] D. P. Dee, S. M. Uppala, A. J. Simmons, P. Berrisford, P. Poli, S. Kobayashi,U. Andrae, M. A. Balmaseda, G. Balsamo, P. Bauer, P. Bechtold, A. C. M. Beljaars,L. van de Berg, J. Bidlot, N. Bormann, C. Delsol, R. Dragani, M. Fuentes, A. J.Geer, L. Haimberger, S. B. Healy, H. Hersbach, E. V. Holm, L. Isaksen, P. Kallberg,M. Kohler, M. Matricardi, A. P. McNally, B. M. Monge-Sanz, J.-J. Morcrette, B.-K.Park, C. Peubey, P. de Rosnay, C. Tavolato, J.-N. Thepaut, F. Vitart, The ERA-Interim reanalysis: configuration and performance of the data assimilation system,Quarterly Journal of the Royal Meteorological Society 137 (656) (2011) 553–597.doi:10.1002/qj.828.

[98] European Transmission System Operators, Yearly Statistics & Adequacy Retro-spect 2013 background data, https://www.entsoe.eu/Documents/Publications/Statistics/YSAR/160112_YSAR_2013_data.zip (2016).

[99] Integration of Renewable Energy in Europe, Tech. rep., Imperial Col-lege, NERA, DNV GL, https://ec.europa.eu/energy/sites/ener/files/

documents/201406_report_renewables_integration_europe.pdf (2014).

[100] T. Ackermann, S. Untsch, M. Koch, H. Rothfuchs, Verteilnetzstudie Rheinland-Pfalz, 2014, https://www.oeko.de/oekodoc/1885/2014-008-de.pdf.

[101] K. Knorr, et al., Kombikraftwerk 2: Abschlussbericht, Tech. rep., Fraunhofer IWESand others (Aug. 2014).

116



http://www.gurobi.com

http://www.gurobi.com


http://www.eea.europa.eu/data-and-maps/data/natura-7

http://www.eea.europa.eu/data-and-maps/data/natura-7

http://dx.doi.org/10.1002/qj.828

https://www.entsoe.eu/Documents/Publications/Statistics/YSAR/160112_YSAR_2013_data.zip

https://www.entsoe.eu/Documents/Publications/Statistics/YSAR/160112_YSAR_2013_data.zip

https://ec.europa.eu/energy/sites/ener/files/documents/201406_report_renewables_integration_europe.pdf

https://ec.europa.eu/energy/sites/ener/files/documents/201406_report_renewables_integration_europe.pdf

https://www.oeko.de/oekodoc/1885/2014-008-de.pdf

Bibliography

[102] Deutsche Energie-Agentur, dena-Studie Systemdienstleistungen 2030, Tech.rep., DENA, online at https://www.dena.de/themen-projekte/projekte/

energiesysteme/dena-studie-systemdienstleistungen-2030/ (2014).

[103] H. Urdal, R. Ierna, J. Zhu, C. Ivanov, A. Dahresobh, D. Rostom, System strengthconsiderations in a converter dominated power system, IET Renewable Power Gen-eration 9 (2015) 10–17(7). doi:10.1049/iet-rpg.2014.0199.

[104] European Environment Agency, National emissions reported to the UNFCCC andto the EU Greenhouse Gas Monitoring Mechanism, https://www.eea.europa.eu/ds_resolveuid/d2a35821365d4ce09b277ab3a85bf305, online, retrieved Sept 2017(2017).

[105] D. Jacob, J. Petersen, B. Eggert, A. Alias, O. B. Christensen, L. M. Bouwer,A. Braun, A. Colette, M. Deque, G. Georgievski, E. Georgopoulou, A. Gobiet,L. Menut, G. Nikulin, A. Haensler, N. Hempelmann, C. Jones, K. Keuler, S. Kovats,N. Kroner, S. Kotlarski, A. Kriegsmann, E. Martin, E. van Meijgaard, C. Moseley,S. Pfeifer, S. Preuschmann, C. Radermacher, K. Radtke, D. Rechid, M. Rounsevell,P. Samuelsson, S. Somot, J.-F. Soussana, C. Teichmann, R. Valentini, R. Vautard,B. Weber, P. Yiou, EURO-CORDEX: new high-resolution climate change projec-tions for European impact research, Regional Environmental Change 14 (2) (2014)563–578. doi:10.1007/s10113-013-0499-2.

[106] M. Schlott, The impact of climate change on European power system optimality,Master’s thesis, Frankfurt Institute for Advances Studies (FIAS), in preparation(2017).

117

https://www.dena.de/themen-projekte/projekte/energiesysteme/dena-studie-systemdienstleistungen-2030/

https://www.dena.de/themen-projekte/projekte/energiesysteme/dena-studie-systemdienstleistungen-2030/

http://dx.doi.org/10.1049/iet-rpg.2014.0199

https://www.eea.europa.eu/ds_resolveuid/d2a35821365d4ce09b277ab3a85bf305

https://www.eea.europa.eu/ds_resolveuid/d2a35821365d4ce09b277ab3a85bf305

http://dx.doi.org/10.1007/s10113-013-0499-2

Acknowledgements

I want to thank Prof. Stefan Schramm for giving me the opportunity to obtain my PhDin his group at the FIAS, his constant and vivid interest in my field of research, and theopportunities to present my research at international conferences.

I also want to thank Prof. Martin Greiner from the University of Aarhus for introducingme to this interesting field of research, his scientific support during my work, and numerousinteresting discussions. I also very much enjoyed my visits to Aarhus and I am very gratefulfor the chance to interact so much with him and his group.

Special thanks go to Dr. Tom Brown, who supported me on my way to disentangle thedifficulties of modelling energy networks and paper writing, and the good time we hadtogether. I learned a lot of interesting things from you!

Changing research field and cities is always challenging, and therefore I want to thankSarah Becker for helping me to find my ways around the new topic, the FIAS and Frank-furt. I very much appreciated you support and guidance.

Furthermore, I would like to thank the whole complex network group at the FIAS,especially Mirko Schafer, Alexander Kies, and Jonas Horsch, for the scientific discussionsand the fun we had together. It was great working with you!

Writing a PhD thesis is a time-consuming and demanding project, and thus a big thanksis due to my wonderful family, for their constant moral support and the deep and lastingtrust they have in my abilities. Without you, none of this would have been possible.